Determining codebooks for different memory areas of a storage device

ABSTRACT

A storage device may program data differently for different memory areas of a memory. In some embodiments, the storage device may use different codebooks for different memory areas. In other embodiments, the storage device may modify bit orders differently for different memory areas. What codebook the storage device uses or what bit order modification the storage device performs for a particular memory area may depend on the bad storage locations specific to that memory area. Where different codebooks are used, optimal codebooks may be selected from a library, or codebooks may be modified based on the bad storage locations of the memory areas.

BACKGROUND

Memory systems may encode and decode data with parity bits that provideredundancy and error correction capability for the data when read fromthe memory. Encoding schemes to encode the data may be based on thepresumption that errors in the data bits when reading the data areevenly distributed across the memory. However, in actuality, the errorsnot usually evenly distributed, which may be due to error-prone orunreliable storage locations not being evenly distributed across thememory. Incorporating information about the unreliable storage locationsinto encoding and decoding schemes in order to improve decodingperformance may be desirable.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of this specification illustrate various aspects of the inventionand together with the description, serve to explain its principles.Wherever convenient, the same reference numbers will be used throughoutthe drawings to refer to the same or like elements.

FIG. 1A is a block diagram of an example non-volatile memory system.

FIG. 1B is a block diagram of a storage module that includes a pluralityof non-volatile memory systems.

FIG. 1C is a block diagram of a hierarchical storage system.

FIG. 2A is a block diagram of example components of a controller of thenon-volatile memory system of FIG. 1A.

FIG. 2B is a block diagram of example components of a non-volatilememory die of the non-volatile memory system of FIG. 1A.

FIG. 3 is a circuit schematic diagram of an example NAND-type flashmemory array.

FIG. 4 is a block diagram of an example organizational arrangement orhierarchy of a memory array for flash memory.

FIG. 5 is a block diagram of example modules of the controller of FIG.2A used to perform an encoding process.

FIG. 6 is a schematic diagram of a generic layout of a parity-checkmatrix.

FIG. 7 is a schematic diagram of a partially completed Tanner graphcorresponding to the parity-check matrix of FIG. 6.

FIG. 8 is a block diagram of an example embodiment of components thatmay be used to evaluate and select codebooks based on decoding metrics.

FIG. 9 is a flow chart of an example method of selecting codebooks basedon decoding metrics.

FIG. 10 is a flow chart of an example method of performing a codebookevaluation process for a particular memory area during normal operationof the memory system of FIGS. 1A-2B.

FIG. 11 is a block diagram of an example embodiment of components thatmay be used to evaluate and score different codebooks for various memoryareas of the memory system of FIGS. 1A-2B.

FIG. 12A is a schematic diagram of a bipartite graph of a low densityparity check code.

FIG. 12B is a schematic diagram of a lifted graph corresponding to thebipartite graph of FIG. 12A.

FIG. 13 is a flow chart of an example method of calculating a codebookscore for a given codebook and a given memory area.

FIG. 14 is a flow chart of an example method of selecting a codebookfrom a plurality of codebooks for each of a plurality of memory areas ofthe memory system of FIGS. 1A-2B based on a scoring scheme.

FIG. 15 is a block diagram of an example embodiment of components thatmay be involved in a codebook modification or permuting process based onbad storage locations.

FIG. 16A shows a schematic diagram of an example Tanner graph of anexisting codebook to be modified.

FIG. 16B shows a schematic diagram of an example Tanner graph of amodified version of the existing codebook of FIG. 16A, which wasmodified based on numbers of bad variable nodes connected to checknodes.

FIG. 17A shows a schematic diagram of another example Tanner graph of anexisting codebook to be modified.

FIG. 17B shows a schematic diagram of an example Tanner graph of amodified version of the existing codebook of FIG. 17A, which wasmodified based on numbers of bad variables participating in minimalcycles.

FIG. 18 is a flow chart of an example method of codebook modification.

FIG. 19 is a block diagram of an example embodiment of components thatmay be involved in determining sizes of codebooks and determiningcodebooks based on the sizes.

FIG. 20A is a block diagram of an example configuration of components ofa parity bit generator module of FIG. 5 that may be configured togenerate sub-code parity bits for information bit sequence portions of acodeword.

FIG. 20B is a schematic diagram of a plurality of sub-codebooks used togenerate sub-codewords of a codeword.

FIG. 20C is a schematic diagram of parity-check sub-matrices and a jointsub-matrix being integrated as part of a larger parity-check matrix.

FIG. 21 is a block diagram of an example embodiment of components thatmay be involved in determining sizes of sub-codebooks and determiningsub-codebooks based on the sizes.

FIG. 22 is a flow chart of an example method of a codebook determinationprocess that may determine codebooks based on size determinations forthe codebooks for a plurality of memory areas.

FIG. 23 is a flow chart of an example method of a sub-codebookdetermination process that may determine sub-codebooks based on sizedeterminations for the sub-codebooks for a plurality of memory areas.

FIG. 24 is a block diagram of an example embodiment of components thatmay be involved in codeword modification based on bad storage locationinformation of a memory area.

FIG. 25 is a flow chart of an example method of performing codewordmodification based on bad storage location information.

DETAILED DESCRIPTION OF EMBODIMENTS

Overview

By way of introduction, the below embodiments relate to memory systemsand methods for encoding and decoding data that includes bits stored inmemory elements identified as unreliable. In one embodiment, a codebookevaluation method is performed. The method includes: identifying, withat least one controller, a first optimal codebook for encoding data tobe stored in a first memory area of a memory of a storage device, thefirst optimal codebook identified from among a plurality of codebooksstored in a codebook library; identifying, with the at least onecontroller, a second optimal codebook among the plurality of codebooksfor encoding data to be stored in a second memory area of the memory,the second memory area having different bad storage locations than thefirst memory area; and storing, in a codebook database of the storagedevice, the first optimal codebook, the second optimal codebook, andinformation associating the first optimal codebook with the first memoryarea and the second optimal codebook with the second memory area.

In some embodiments, the method includes: programming, with the at leastone controller, first data into the first memory area using theplurality of codebooks; after programming the first data, reading, withthe at least one controller, the first data from the first memory areaand decoding, with the at least one controller, the first data using theplurality of codebooks; and identifying, with the at least onecontroller, decoding metrics associated with each of the plurality ofcodebooks for the first memory area based on the decoding, whereidentifying the first optimal codebook includes identifying the firstoptimal codebook from the plurality of codebooks based on the decodingmetrics.

In some embodiments, the method includes, after identifying the firstoptimal codebook, detecting, with the at least one controller, atriggering event that triggers the at least one controller to checkwhether a codebook more optimal than the first optimal codebook isstored in the codebook database; in response to the detecting, encoding,with the at least one controller, one or more other codebooks in thecodebook database other than the first optimal codebook; programming,with the at least one controller, the encoded test data into a test areaof the first memory area; decoding, with the at least one controller,the encoded test data using the one or more other codebooks;determining, with at least one controller, that a codebook of the one ormore other codebooks provides better decoding metrics than the firstoptimal codebook for the first memory area; and updating, with at leastone controller, the codebook database to indicate to encode futureinformation bit sequences to be stored in the first memory area with thecodebook of the one or more other codebooks instead of the first optimalcodebook.

In some embodiments, the method includes: identifying, with the at leastone controller, bad storage location information of the first memoryarea; scoring, with the at least one controller, the plurality ofcodebooks in the codebook library for the first memory area based on thebad storage location information of the first memory area; andidentifying, with the at least one controller, that the first optimalcodebook has a best score among the plurality of codebooks in thecodebook library for the first memory area, wherein identifying thefirst optimal codebook for the first memory area is based on identifyingthat the first optimal codebook has the best score.

In some embodiments, ranking the plurality of codebooks includes, foreach codebook of the plurality of codebooks, calculating, with the atleast one controller, expected contributions to a decoding errorprobability of a cycle set for connections of variable nodes and checknodes.

In some embodiments, calculating the expected contributions to adecoding error probability comprises calculating the expectedcontributions with the codebooks in their lifted form.

In some embodiments, calculating the expected contributions to adecoding error probability is based on different bit erasure probabilityvalues depending on whether associated variable nodes are good variablenodes or bad variable nodes.

In some embodiments, calculating the expected contributions to adecoding error probability comprises, for a given expected contributioncalculation corresponding to a given variable node connected to a givencheck node, selecting, with the at least one controller, a high erasureprobability value where the given variable node is a bad variable nodeand a low erasure probability value where the given variable node is agood variable node.

In some embodiments, the first memory area and the second memory areaare part of a plurality of different memory areas, where the differentmemory areas includes different dies, different planes, differentblocks, different pages, or different segments of the memory.

In another embodiment, a codebook modification method is performed. Themethod includes: identifying, with at least one controller, bad storagelocation information of a memory area of a plurality of different memoryareas of a storage device; accessing, with the at least one controller,an existing codebook in a codebook database; modifying, with the atleast one controller, the existing codebook to generate a modifiedcodebook based on the bad storage location information; and storing, ina codebook database of the storage device, the modified codebook andassociation information associating the modified codebook with thememory area, where the storage device is configured to encode data to bestored in the memory area using the modified codebook in response to thestoring of the modified codebook and the association information in thecodebook database.

In some embodiments, the method includes: selecting, with the at leastone controller, a check node of the existing codebook for codebookmodification based on numbers of bad variable nodes connected to checknodes of the existing codebook, where modifying the existing codebookcomprises changing a configuration of connections to the check node thatreduces a number of connections of bad variable nodes to the check node.

In some embodiments, the existing codebook has an associatedparity-check matrix, and changing the configuration of connections tothe check node includes: removing one or more bad connections to thecheck node from the existing codebook or swapping one or more badconnections to the check node with a good connection connected toanother node of the check nodes.

In some embodiments, the existing codebook has an associatedparity-check matrix, and modifying the existing codebook includesswapping, with the at least one controller, a first column of theparity-check matrix corresponding to a bad variable node connected tothe selected check node with a second column of the parity check matrixcorresponding to a good variable node unconnected with the selectedcheck node.

In some embodiments, the method includes: selecting, with the at leastone controller, a bad variable node of the existing codebook forcodebook modification based on numbers of bad variable nodesparticipating in minimal cycles of the existing codebook, wheremodifying the existing codebook includes changing a configuration ofconnections connected to the bad variable node so that a minimal cycleinvolving the variable node is removed.

In some embodiments, the method includes: identifying, with the at leastone controller, the minimal cycle based on a criterion derived from atleast one of a number of bad variable nodes participating in the minimalcycle, a length of the minimal cycle, or a total number of variablenodes participating in the minimal cycle.

In another embodiment, a codebook determination method is performed. Themethod includes: identifying, with at least one controller, a memoryarea of a plurality of memory areas, wherein a plurality of codebooksare used to encode data stored in the memory area; identifying, with theat least one controller, bad storage location information of the memoryarea; identifying, with the at least one controller, respective numbersof parity bits each of the plurality of codebooks are to generate toencode data stored in the memory area, the respective numbers beingbased on the bad storage location information; determining, with the atleast one controller, the plurality of codebooks according to therespective numbers; and loading, with the at least one controller, theplurality of codebooks into a codebook database of a memory system.

In some embodiments, the respective numbers of parity bits that thecodebooks are configured to generate are based on a ratio of a number ofgenerated parity bits to a number of bad storage locations in a storageunit.

In some embodiments, the respective numbers of parity bits that thecodebooks are configured to generate are based on a ratio of a number ofgenerated parity bits to a number of bad storage locations in a storagesub-unit.

In some embodiments, the memory area includes a plurality of storageunits of a same storage page, wherein each of the plurality of codebooksis configured to encode data for a respective one of the storage units,and the method includes: calculating, with the at least one controller,mutual information for each of the storage units based on respectivenumbers of bad storage locations in each of the storage units, whereidentifying the respective numbers of parity bits is based on the mutualinformation calculated for each of the storage units.

In some embodiments, the memory area includes a plurality of storagesub-units of a same storage unit, where the plurality of codebookscomprises a plurality of sub-codebooks, each of the plurality ofsub-codebooks is configured to encode data for a respective one of thestorage sub-units, and the method includes: calculating, with the atleast one controller, mutual information for each of the storagesub-units based on respective numbers of bad storage locations in eachof the storage sub-units, where identifying the respective numbers ofparity bits is based on the mutual information calculated for each ofthe storage sub-units.

In some embodiments, the memory area includes a storage page or astorage unit, and where at least two of the plurality of codebooks areconfigured to generate different numbers of parity bits from each other.

Other embodiments are possible, and each of the embodiments can be usedalone or together in combination. Accordingly, various embodiments willnow be described with reference to the attached drawings.

Embodiments

The following embodiments describe non-volatile memory systems andrelated methods for encoding and decoding data that includes bits storedor to be stored in memory elements identified as unreliable. Beforeturning to these and other embodiments, the following paragraphs providea discussion of exemplary non-volatile memory systems and storagemodules that can be used with these embodiments. Of course, these arejust examples, and other suitable types of non-volatile memory systemsand/or storage modules can be used.

FIG. 1A is a block diagram illustrating a non-volatile memory system100. The non-volatile memory system 100 may include a controller 102 andnon-volatile memory that may be made up of one or more non-volatilememory dies 104. As used herein, the term die refers to the set ofnon-volatile memory cells, and associated circuitry for managing thephysical operation of those non-volatile memory cells, that are formedon a single semiconductor substrate. The controller 102 may interfacewith a host system and transmit command sequences for read, program, anderase operations to the non-volatile memory die(s) 104.

The controller 102 (which may be and/or referred to as a flash memorycontroller) can take the form of processing circuitry, a microprocessoror processor, and a computer-readable medium that storescomputer-readable program code (e.g., software or firmware) executableby the (micro)processor, logic gates, switches, an application specificintegrated circuit (ASIC), a programmable logic controller, and anembedded microcontroller, for example. The controller 102 can beconfigured with hardware and/or firmware to perform the variousfunctions described below and shown in the flow diagrams. Also, some ofthe components shown as being internal to the controller can also bestored external to the controller, and other components can be used.Additionally, the phrase “operatively in communication with” could meandirectly in communication with or indirectly (wired or wireless) incommunication with through one or more components, which may or may notbe shown or described herein.

The controller 102 may be configured to manage data stored in the memory104 and communicate with a host, such as a computer or electronicdevice. The controller 102 may have various functionality in addition tothe specific functionality described herein. For example, the controller102 can format the memory 104 to ensure that the memory 104 is operatingproperly, map out bad flash memory cells, and allocate spare cells to besubstituted for future failed cells. Some part of the spare cells can beused to hold firmware to operate the controller 102 and implement otherfeatures. In operation, when a host needs to read data from or writedata to the memory 104, it will communicate with the controller 102. Ifthe host provides a logical address to which data is to be read/written,the controller 102 can convert the logical address received from thehost to a physical address in the memory 104. (Alternatively, the hostcan provide the physical address). The controller 102 can also performvarious memory management functions, such as, but not limited to, wearleveling (distributing writes to avoid wearing out specific blocks ofmemory that would otherwise be repeatedly written to) and garbagecollection (after a block is full, moving only the valid pages of datato a new block, so the full block can be erased and reused).

The interface between the controller 102 and the non-volatile memorydie(s) 104 may be any suitable flash interface, such as Toggle Mode 200,400, or 800 as non-limiting examples. In one embodiment, the memorysystem 100 may be a card based system, such as a secure digital (SD) ora micro secure digital (micro-SD) card. In an alternate embodiment, thesystem 100 may be part of an embedded memory system.

The non-volatile memory system 100 may include a single channel betweenthe controller 102 and the non-volatile memory die(s) 104, or multiple(e.g., 2, 4, 8 or more) channels between the controller 102 and the NANDmemory die(s) 104. How many channels exist may depend on variousfactors, such as the capabilities of the controller 102, the number ofmemory dies 104, and/or layout or organization of the memory elements inthe memory dies 104, as non-limiting examples. In any of the embodimentsdescribed herein, more than a single channel may exist between thecontroller and the memory die(s)s 104, even if a single channel is shownin the drawings.

FIG. 1B illustrates a storage module 200 that includes pluralnon-volatile memory systems 100. As such, the storage module 200 mayinclude a storage controller 202 that interfaces with a host and with astorage system 204, which includes a plurality of non-volatile memorysystems 100. The interface between the storage controller 202 andnon-volatile memory systems 100 may be a bus interface, such as a serialadvanced technology attachment (SATA), a peripheral component interfaceexpress (PCIe) interface, an embedded MultiMediaCard (eMMC) interface, aSD interface, or a Universal Serial Bus (USB) interface, as examples.The storage system 200, in one embodiment, may be a solid state drive(SSD), such as found in portable computing devices, such as laptopcomputers and tablet computers, and mobile phones.

FIG. 1C is a block diagram illustrating a hierarchical storage system210. The hierarchical storage system 210 may include a plurality ofstorage controllers 202, each of which control a respective storagesystem 204. Host systems 212 may access memories within the hierarchicalstorage system 210 via a bus interface. Example bus interfaces mayinclude a non-volatile memory express (NVMe), a fiber channel overEthernet (FCoE) interface, an SD interface, a USB interface, a SATAinterface, a PCIe interface, or an eMMC interface as examples. In oneembodiment, the storage system 210 illustrated in FIG. 1C may be a rackmountable mass storage system that is accessible by multiple hostcomputers, such as would be found in a data center or other locationwhere mass storage is needed.

FIG. 2A is a block diagram illustrating exemplary components of thecontroller 102 in more detail. The controller 102 may include a frontend module 108 that interfaces with a host, a back end module 110 thatinterfaces with the non-volatile memory die(s) 104, and various othermodules that perform various functions of the non-volatile memory system100.

In general, as used herein, a module may be hardware or a combination ofhardware and software. For example, each module may include anapplication specific integrated circuit (ASIC), a field programmablegate array (FPGA), a circuit, a digital logic circuit, an analogcircuit, a combination of discrete circuits, gates, or any other type ofhardware or combination thereof. In addition or alternatively, eachmodule may include memory hardware that comprises instructionsexecutable with a processor or processor circuitry to implement one ormore of the features of the module. When any one of the module includesthe portion of the memory that comprises instructions executable withthe processor, the module may or may not include the processor. In someexamples, each module may just be the portion of the memory thatcomprises instructions executable with the processor to implement thefeatures of the corresponding module without the module including anyother hardware. Because each module includes at least some hardware evenwhen the included hardware comprises software, each module may beinterchangeably referred to as a hardware module.

The controller 102 may include a buffer manager/bus controller module114 that manages buffers in random access memory (RAM) 116 and controlsthe internal bus arbitration for communication on an internalcommunications bus 117 of the controller 102. A read only memory (ROM)118 may store and/or access system boot code. Although illustrated inFIG. 2A as located separately from the controller 102, in otherembodiments one or both of the RAM 116 and the ROM 118 may be locatedwithin the controller 102. In yet other embodiments, portions of RAM 116and ROM 118 may be located both within the controller 102 and outsidethe controller 102. Further, in some implementations, the controller102, the RAM 116, and the ROM 118 may be located on separatesemiconductor dies.

Additionally, the front end module 108 may include a host interface 120and a physical layer interface (PHY) 122 that provide the electricalinterface with the host or next level storage controller. The choice ofthe type of the host interface 120 can depend on the type of memorybeing used. Examples types of the host interface 120 may include, butare not limited to, SATA, SATA Express, SAS, Fibre Channel, USB, PCIe,and NVMe. The host interface 120 may typically facilitate transfer fordata, control signals, and timing signals.

The back end module 110 may include an error correction controller (ECC)engine 124 that encodes the data bytes received from the host, anddecodes and error corrects the data bytes read from the non-volatilememory 104. The back end module 110 may also include a command sequencer126 that generates command sequences, such as program, read, and erasecommand sequences, to be transmitted to the non-volatile memory die(s)104. Additionally, the back end module 110 may include a RAID (RedundantArray of Independent Drives) module 128 that manages generation of RAIDparity and recovery of failed data. The RAID parity may be used as anadditional level of integrity protection for the data being written intothe non-volatile memory system 100. In some cases, the RAID module 128may be a part of the ECC engine 124. A memory interface 130 provides thecommand sequences to the non-volatile memory die(s) 104 and receivesstatus information from the non-volatile memory die(s) 104. Along withthe command sequences and status information, data to be programmed intoand read from the non-volatile memory die(s) 104 may be communicatedthrough the memory interface 130. In one embodiment, the memoryinterface 130 may be a double data rate (DDR) interface, such as aToggle Mode 200, 400, or 800 interface. A flash control layer 132 maycontrol the overall operation of back end module 110.

Additional modules of the non-volatile memory system 100 illustrated inFIG. 2A may include a media management layer 138, which performs wearleveling of memory cells of the non-volatile memory die 104. Thenon-volatile memory system 100 may also include other discretecomponents 140, such as external electrical interfaces, external RAM,resistors, capacitors, or other components that may interface withcontroller 102. In alternative embodiments, one or more of the RAIDmodule 128, media management layer 138 and buffer management/buscontroller 114 are optional components that may not be necessary in thecontroller 102.

FIG. 2B is a block diagram illustrating exemplary components of anon-volatile memory die 104 in more detail. The non-volatile memory die104 may include a non-volatile memory array 142. The non-volatile memoryarray 142 may include a plurality of non-volatile memory elements orcells, each configured to store one or more bits of data. Thenon-volatile memory elements or cells may be any suitable non-volatilememory cells, including NAND flash memory cells and/or NOR flash memorycells in a two dimensional and/or three dimensional configuration. Thememory cells may take the form of solid-state (e.g., flash) memory cellsand can be one-time programmable, few-time programmable, or many-timeprogrammable. In addition, the memory elements or cells may beconfigured as single-level cells (SLCs) that store a single bit of dataper cell, multi-level cells (MLCs) that store multiple bits of data percell, or combinations thereof. For some example configurations, themulti-level cells (MLCs) may include triple-level cells (TLCs) thatstore three bits of data per cell.

Additionally, for some example configurations, a flash memory cell mayinclude in the array 142 a floating gate transistor (FGT) that has afloating gate and a control gate. The floating gate is surrounded by aninsulator or insulating material that helps retain charge in thefloating gate. The presence or absence of charges inside the floatinggate may cause a shift in a threshold voltage of the FGT, which is usedto distinguish logic levels. That is, each FGT's threshold voltage maybe indicative of the data stored in the memory cell. Hereafter, FGT,memory element and memory cell may be used interchangeably to refer tothe same physical entity.

The memory cells may be disposed in the memory array 142 in accordancewith a matrix-like structure of rows and columns of memory cells. At theintersection of a row and a column is a memory cell. A column of memorycells may be referred to as a string. Memory cells in a string or columnmay be electrically connected in series. A row of memory cells may bereferred to as a page. Control gates of FGTs in a page or row may beelectrically connected together.

The memory array 142 may also include wordlines and bitlines connectedto the memory cells. Each page of memory cells may be coupled to awordline. In particular, each wordline may be coupled to the controlgates of FGTs in a page. In addition, each string of FGTs may be coupledto a bitline. Further, a single string may span across multiplewordlines, and the number of FGTs in a string may be equal to the numberof pages in a block.

FIG. 3 is a circuit schematic diagram of at least a portion of anexemplary NAND-type flash memory array 300, which may be representativeof at least a portion of the memory array 142. The memory array portion300 may include a P-number of series-connected strings of (N times M)FGTs, each coupled to one of a P-number of bitlines BL₁ to BL_(P-1),where N is the number of blocks 308 ₀ to 308 _(N-1) in the memory array300, and M is the number of pages of FGTs coupled to wordlines WL ineach of the N-number of blocks 308 ₀ to 308 _(N-1).

To sense data from the FGTs, a page of FGTs and a corresponding wordlinemay be selected, and current sensing of bitlines may be employed todetermine whether a floating gate of a FGT in the selected page containscharge or not. Current that flows through a string may flow from asource line SL, through the string, to a bitline BL to which the stringis coupled. The string may be coupled to the source line SL via a sourceselect transistor, and may be coupled to its associated bitline BL via adrain select transistor. For example, a first string of FGTs 302_((0,0)) to 302 _((NM-1,0)) may be coupled to the source line SL via asource select transistor 304 ₀ that is connected to the source line SL,and may be coupled to its associated bitline BL₀ via a drain selecttransistor 306 ₀. The other strings may be similarly coupled. Switchingof source select transistors 304 ₀, 304 ₁, . . . , 304 _(P-1) may becontrolled using a source select gate bias line SSG that supplies asource select gate bias voltage V_(SSG) to turn on an off the sourceselect transistors 304 ₀, 304 ₁, . . . , 304 _(P-1). Additionally,switching of drain select transistors 306 ₀, 306 ₁, . . . , 306 _(P-1)may be controlled using a drain select gate bias line DSG that suppliesa drain select gate bias voltage V_(DSG) to turn on and off the drainselect transistors 306 ₀, 306 ₁, . . . , 306 _(P-1).

Referring back to FIG. 2B, the non-volatile memory die 104 may furtherinclude a page buffer or data cache 144 that caches data that is sensedfrom and/or that is to be programmed to the memory array 142. Thenon-volatile memory die 104 may also include a row address decoder 146and a column address decoder 148. The row address decoder 146 may decodea row address and select a particular wordline in the memory array 142when reading or writing data to/from the memory cells in the memoryarray 142. The column address decoder 148 may decode a column address toselect a particular group of bitlines in the memory array 142 to beelectrically coupled to the data cache 144.

In addition, the non-volatile memory die 104 may include peripheralcircuitry 150. The peripheral circuitry 150 may include a state machine152 that may be configured to control memory operations performed on thedie 104 and provide status information to the controller 102. Theperipheral circuitry 150 may also include volatile memory 154. Anexample configuration of the volatile memory 154 may include latches,although other configurations are possible.

Referring to FIG. 4, the memory array 142 and/or a plurality of memoryarrays 142 spanning multiple memory dies 104 may have an organizationalarrangement or hierarchy under which memory cells of the memory array142 and/or multiple memory arrays 142 of multiple memory dies 104 may beorganized. The controller 102 may be configured to store and access datain accordance with the organizational arrangement or hierarchy.

FIG. 4 is a block diagram of an example organizational arrangement orhierarchy of a memory array 142 for flash memory. As mentioned, forflash memory, the memory cells may be divided or organized into blocks402, and each block 402 may further be divided into a number of pages404. Each block 402 may contain the minimum number of memory elementsthat may be erased together. In addition, each page 404 may be a unit ofsensing in the memory array 142. Each individual page 404 may further bedivided into segments or units 406, with each segment or unit 406containing the fewest number of memory cells that may be written to atone time as a basic programming operation. Data stored in a segment orunit of memory cells—referred to as a flash memory unit (FMU), an ECCpage, or a codeword—may contain the amount of data that is written atone time during a basic programming operation and/or the amount of datathat can be encoded or decoded by the ECC engine 124 during a singleencoding or decoding operation. The pages 404 may be divided into thesame number of segments or units. Example numbers of segments or unitmay be four or eight, although other numbers are possible. In general,data may be stored in blocks and pages of memory elementsnon-contiguously (randomly) or contiguously.

In addition, the organizational arrangement or hierarchy may include oneor more planes in which each of the blocks 402 may be configured.Generally, a plane includes a “column” of blocks 402 or pages 404,although other configurations may be possible. A single memory array 142may include a single plane or multiple planes. The example arrangementshown in FIG. 4 includes two planes, Plane 0 and Plane 1. Data stored indifferent planes may be sensed simultaneously or independently. Also,some organizational arrangements or hierarchies may include sub-planes.For example, each plane may include multiple sub-planes. In general, asub-plane may include a “column” of units 406. The number of sub-planeswithin a single plane may depend on the number of units 406 within asingle page 404. For example, as shown in FIG. 4, for configurationswhere a page 404 includes four units 406, then there may be foursub-planes within a single plane, such as four sub-planes within Plane 0and/or four sub-planes within Plane 1.

Additionally, the organizational arrangement or hierarchy may includemetablocks 408 and metapages 410. A metablock address or numberidentifying a metablock may be mapped to and/or correspond to a logicaladdress (e.g., a logical group number) provided by a host. A metablock408 and a metapage 410 may span or be distributed across a respectivesingle block and page in a single plane, or alternatively, may span orbe distributed across respective multiple blocks and multiple pagesacross multiple planes. FIG. 4 shows the metablock 408 and the metapage410 spanning across two planes, Plane 0 and Plane 1. Depending on theorganizational arrangement, metablocks 408 and metapages 410 spanningacross multiple planes may span across only those planes of a singlememory die 104, or alternatively may span across multiple planes locatedof multiple memory dies 104.

Referring back to FIG. 3, the organizational arrangement or hierarchymay also group the bitlines (BL) into groups (otherwise referred to ascolumns) of bitlines (BL). Grouping the bitlines may reduce thecomplexity of addressing the storage locations of the array in that acolumn address over a page may be identified on the basis of groups (orcolumns) of bitlines, rather than on a bitline-by-bitline basis. In oneexample, a block 308 may include 16,000 bitlines (i.e., P=16,000), andevery sixteen bitlines BL may be grouped together in a group (orcolumn). Grouping the 16,000 bitlines BLs into groups or columns ofsixteen may yield only 1,000 column addresses over a page, rather than16,000 column addresses.

At some point during the lifetime of the non-volatile memory system 100,some of the memory elements of an array may store data unreliably (e.g.,be determined to store data more unreliably than reliably). The memoryelements may store data unreliably from the beginning of its life, suchas upon being manufactured, or may initially store data reliably, butmay then store data unreliably after a period of operation. There may bevarious reasons why these memory elements store data unreliably, such asdue to open circuits, closed circuits, short circuits, endurance orretention issues (e.g., a memory element has exceeded a certainthreshold number of program/erase cycles), or as a result of programdisturb (when a bit is programmed into a memory element and then later,a neighboring memory element (from the same wordline or an adjacentwordline) is programmed at a higher state, causing the first memoryelement to be programmed at a slightly higher state). Whatever thereason, memory elements may be or become unreliable, and as a result maynot reliably return data at the values at which the data was programmed.

For purposes of the present description, the term “bad” or “weak” may beused interchangeably with “unreliable.” Accordingly, the term “bad” or“weak” may be used in conjunction with various storage locations orcomponents of an array (e.g., memory elements, bit lines, bitlinegroups, or other groupings or zones of memory elements) to indicatethose storage locations or components as unreliable and/or that are atleast identified in the non-volatile memory system 100 as beingunreliable or “weak”. Similarly, the term “good” or “strong” may be usedto refer to reliable storage locations or components and/or that areidentified in the non-volatile memory system 100 as being reliable. Inaddition, the terms “bad,” “weak,” “good” and “strong” may be used inconjunction with data (including bits of data) to indicate that the datais to be stored or is being stored in reliable and unreliable storagelocations, respectively.

In some situations, memory elements coupled to the same bitline may besimilarly unreliable. That is, if one memory element coupled to aparticular bitline is unreliable, the other memory elements that arecoupled to that bitline may also be unreliable. Accordingly, thecontroller 102 may be configured to identify unreliable memory elementson a bitline basis. If the controller 102 identifies a bitline asunreliable, it may presume that all of the memory elements coupled tothat bitline are bad, less reliable, weak, or unreliable. In addition,if the controller 102 identifies a particular memory element asunreliable, it may presume that the other memory elements coupled to thesame bitline are also unreliable and identify that bitline as anunreliable or bad bitline. Also, if the controller 102 does not identifyany memory elements in a bitline as being unreliable, it may identifythat bitline as a reliable or good bitline.

In addition, the controller 102 may be configured to identifyreliable/good and unreliable/bad columns of bitlines. For example, ifthe controller 102 identifies at least one bitline in a column asunreliable, it may identify all of the bitlines in that column as bad,or generally that the column is unreliable or bad. Alternatively, if thecontroller 102 does not identify any bitlines in a column as unreliable,it may identify that as good or reliable.

Bad storage locations may be identified and stored in one or more badstorage databases, which are represented below in the Figures by the badstorage database 1110 in FIG. 11, the bad storage database 1506 in FIGS.15 and 18, the bad storage database 2108 in FIG. 21, and the bad storagedatabase 2206 in FIG. 22. The controller 102 may be configured to accessthe bad storage location database(s) in order to identify the badstorage locations. The bad storage database(s) may identify the badstorage locations as bad columns, bad bitlines, or a combinationthereof. Other ways that the bad storage database(s) may identify thebad storage locations may be possible. Additionally, the bad storagedatabase(s) may be organized and/or managed in various ways. Forexample, upon manufacture of the memory system 100, storage locationsthat are initially identified as being bad may be identified and storedin one database, while storage locations initially identified as goodbut then later identified as bad after operation of the memory system100 may be stored in another database. Alternatively, the bad storagelocations that are initially bad and bad storage locations that laterbecome bad may be combined into a single database. For example, the badstorage database may be initially populated with storage locations thatare initially identified as bad upon manufacture. The controller 102 maythen update the database as it identified bad storage locations uponmanufacture. Various ways of organizing and managing a bad storagedatabase are possible.

In addition, the bad storage database may be stored in any or aplurality of storage locations within the non-volatile memory system 100and/or external to the non-volatile memory system 100. For example, abad storage database may be stored in the array having the storagelocations that the database identifies. Accordingly, for multi-diesystems 100, each die 104 may store an associated bad storage database.Alternatively, one of the dies 104 may store all of the databases forall of the dies 104. Various other configurations for storing the badstorage database(s) for multi-die systems 100 may be possible.Additionally, for some example configurations, the controller 102 may beconfigured to load a copy of the databases(s) into RAM 116 to manage thedatabase(s), such as during initialization and/or when reading and/orwriting data to a particular die 104, and may update the versions of thedatabase(s) stored in the non-volatile memory dies 104 as appropriate.

Some example memory systems encode and decode data without considerationfor the bad storage locations of the memory dies. Such memory systemsmay generally consider the errors that result from reading data to berandom and that such random errors are evenly distributed across thememory dies within a memory system. However, due to the existence of badstorage locations, and that the bad storage locations may be differentfor different memory systems, or different for different dies and/ordifferent planes within a single memory system, the errors are generallynot evenly distributed. Consequently, the same encoding and decodingschemes for different memory areas with different bad bit locations mayresult in different decoding outcomes, with the ECC engine 124 having totake or longer or needing more decoding iterations in order tosuccessfully decode read data for certain store locations compared toother storage locations within the memory dies 104.

In contrast to those memory systems, the non-volatile memory system 100of the present description may encode and decode data according toencoding and decoding schemes that take into consideration the badstorage locations of the memory dies 104. In doing so, the non-volatilememory system 100 may optimize the encoding and decoding for particularmemory areas within the memory dies 104, resulting in improved decodingperformance across the memory dies 104 compared to other memory systemsthat ignore the bad storage locations and use the same encoding anddecoding schemes across all of the memory dies 104.

The non-volatile memory system 100 may take into consideration the badstorage locations of the memory dies 104 in two ways: (1) the memorysystem 100 may use different codebooks to encode and decode data fordifferent memory areas having different bad storage locations, where thecodebooks are optimal for the particular memory areas for which they areused (at least compared to the other codebooks used in the memory system100); or (2) the order of the bit sequence of a given codeword ismodified based on the bad storage locations where the codeword is to bestored in the memory dies 104.

FIG. 5 shows a block diagram of components a first example embodiment ofthe controller 102 that may be involved in an encoding process of awrite operation to write data into a non-volatile memory die 104. Forsome example configurations, the components other than the RAM 116 maybe components of the ECC engine 124, although in other exampleconfigurations, some or all of these components may be consideredcomponents separate from the ECC engine 124. In addition to the RAM 116,the components involved in the encoding process may include a parity bitgenerator module 502, a codebook selector module 504, and a codebookdatabase 508.

In general, the non-volatile memory system 100 may store data in thememory dies 104 as codewords. Each codeword may include information data(bits) and parity data (bits). The information bits may include payloaddata (bits), which includes the data that the host wants written to andread from the non-volatile memory dies 104. The information bits mayalso include header data (bits), which may include various informationabout the payload data, such as logical address information, the writesource, when the data is written (timestamp), flag fields, reversionnumbers, and scrambler seeds as non-limiting examples. The parity bitsmay be generated during encoding in order to detect and correct errorsof the header and payload portions of the data during a decoding phaseof a read operation to read the data from the non-volatile memory die104.

Prior to the encoding process, the information bits to be written intothe non-volatile memory 104 may be loaded in the RAM 116 in an unencoded(e.g., raw) format. After the information bits are loaded into the RAM116, the parity bit generator module 502 may retrieve the informationbits and generate the parity bits associated with the information bits.

The parity bit generator module 502 may be configured to generate theparity bits using a codebook or code. In a particular exampleconfiguration, the codebook may be a low-density parity-check (LDPC)codebook. For LDPC encoding, an LDPC codebook may correspond to and/orhave associated with it a parity-check matrix H. The parity bitgenerator module 502 may be configured to generate the parity bits suchthat following matrix equation is satisfied:Hω=0,  (1)where H is the parity-check matrix and ω is the codeword including theinformation bits and the parity bits. The codeword ω may be formattedsuch the first K bits of the codeword ω are equal to an information bitsequence β of the information bits, and the last M bits of the codewordω are equal to the parity bit sequence δ of the parity bits. The paritybit generator module 502 may then generate the parity bits such that thefollowing equation is satisfied:

$\begin{matrix}{{H \cdot \begin{bmatrix}\beta \\\delta\end{bmatrix}} = 0.} & (2)\end{matrix}$In some LDPC encoding schemes, the parity bit generator module 502 maygenerate the parity bit sequence δ may be taking advantage of the sparsenature of the parity-check matrix H in accordance with LDPC.

FIG. 6 shows a schematic diagram of a generic layout of a parity-checkmatrix H. The parity-check matrix H may include a first submatrixH_(info) and a second submatrix H_(parity). The first submatrix H_(info)may include a J-number of columns equal to a J-number of bits in theinformation bit sequence β. The second submatrix H_(parity) may includean K-number of columns that is equal to the K-number of bits in theparity bit sequence δ. Also, as shown in FIG. 6, each of the firstsubmatrix H_(info) and the second submatrix H_(parity) have an K-numberof rows equal to the K-number of bits in the parity bit sequence δ.

Additionally, the first submatrix H_(info) and the second submatrixH_(parity) are positioned relative to each other such that the lastcolumn of the first submatrix H_(info) is adjacent to the first columnof the second submatrix H_(parity). Also, the order of the rows arecommon amongst the first and second submatrices H_(info), H_(parity). Inother words, the first row of the first submatrix H_(info) forms acommon row with the first row of the second submatrix H_(parity), and soon. Further, the elements of the first and second submatrices H_(info),H_(parity) (K by J elements for the first submatrix H_(info) and K by Kelements for the second submatrix H_(parity)) may each include binary“0” and “1” values. The makeup of the 0 and 1 values may be inaccordance with various encoding schemes, such as LDPC or Quasi-Cyclic(QC)-LDPC codes, as examples.

The parity-check matrix H may have a corresponding Tanner graph. FIG. 7shows a schematic diagram of a partially completed Tanner graphcorresponding to the parity-check matrix H of FIG. 6. In general, aTanner graph may include variable nodes (or just variables), check nodes(or just checks), and edges connecting the check nodes and the variablesnodes. The number of variable nodes may be equal to the number ofcolumns in the parity-check matrix H and the number of bits in acodeword ω. Accordingly, there may be a J+K number of variable nodesv(1) to v(J+K) corresponding to the J-number of bits in the informationbit sequence β and the K-number of parity bits of the parity bitsequence δ. The number of check nodes may be equal to the number of rowsin the parity-check matrix H and the number of parity bits in the paritybit sequence δ. Accordingly, there may be an K-number of check nodesc(1) to c(K) corresponding to the K-number of parity bits in the paritybit sequence δ. A particular variable node may be connected to aparticular check node via an edge or connection if the element in theparity-check matrix H corresponding to that variable node and that checknode has a 1 value instead of a 0 value. For example, FIG. 7 shows anedge connecting the first variable node v(1) and the first check nodec(1).

Referring back to FIG. 5, the parity bit generator module 502 mayutilize a plurality or an N-number of codebooks 506(1)-506(N) to encodeinformation bits to be stored in the memory dies 104. The codebooks506(1)-506(N) may be different from one another. For example, theparity-check matrices corresponding to the codebooks 506(1)-506(N) maybe different from each other. Two parity-check matrices may be differentfrom each other by having at least one corresponding element with adifferent value. In addition or alternatively, two parity-check matricesmay be different from each other by having different sizes (i.e., adifferent number of rows and/or a different number of columns).

Each of the codebooks 506(1)-506(N) may be associated with one or morememory areas of the memory dies 104. A memory area may be anidentifiable portion with a definable size or boundary, such as oneidentified by the organizational arrangement or hierarchy described withreference to FIG. 4. Examples of a memory area may be a memory die, aplane of a die, sub-plane of a die, a block of a die, a page of a block(e.g., page 404 in FIG. 4), or a unit or segment of a page (e.g., 406 inFIG. 4). Otherwise stated, the N-number of codebooks 506(1)-506(N) maybe assigned or associated with the storage locations of the memory dies104 on a per-die basis, a per-plane basis, a per-block basis, a per-pagebasis, or a per-segment basis.

In order to encode a received information bit sequence β, the parity bitgenerator module 502 may communicate with the codebook selector module504 to receive and/or identify a selected one of the codebooks506(1)-506(N). As shown in FIG. 5, the codebook selector module 504 mayreceive memory address information that identifies where in the memorydies 104 codeword ω, encoded from the information bit sequence β, is tobe stored. In some example configurations, the memory management layermodule 138 (FIG. 2A) may manage and maintain a list of available storageareas (e.g., a free block list). Using the list, the memory managementlayer 138 may be configured to determine where in the memory dies 104the information bit sequence β is to be stored. The memory managementlayer 138 may provide the memory address information to the codebookselector module 504.

In response to receipt of the memory address information, the codebookselector module 504 may be configured to identify a memory areacorresponding to the memory address information. In addition, thecodebook selector module 504 may be configured to determine which of thecodebooks 506(1)-506(N) the identified memory area is associated. Thecodebooks 506(1)-506(N) may be stored and organized in a codebookdatabase 508, and the codebook selector module 504 may be configured toaccess the codebook database 508 to obtain a selected one of thecodebooks 506(1)-506(N) that is associated with the identified memoryarea. In some example configurations, information 507 that associatesthe codebooks 506(1)-506(N) with the various memory areas of the memorydies 104 may also be included and maintained in the codebook database508. The codebook selector module 504 may use and/or access theassociation information 507 to select one of the codebooks506(1)-506(N).

Upon selecting one of the codebooks 506(1)-506(N), the codebook selectormodule 504 may provide the selected codebook to the parity bit generatormodule 502. The parity bit generator module 502 may then use theselected codebook to generate the parity bits δ for the unencodedinformation bit sequence β stored in the RAM 116, such as in accordancewith equations (1) or (2) above. The information bits β and theassociated parity bits δ may be combined to form the codeword ω. Thecodeword ω stored in the RAM 116 may then be provided to the sequencermodule 126, which may send the codeword ω to the memory dies 104 via thememory interface 130. The codeword ω may be stored in a storage locationin the memory dies 104 identified by and/or corresponding to the memoryaddress information that was provided to the codebook selector module504. Although not shown in FIG. 5, the selected codebook from thedatabase 508 used to encode the information bits β may also be used todecode the codeword ω during a decode phase, such as when the codeword ωis read from the memory dies 104.

As previously mentioned, the different memory areas within the memorydies 104 may have different bad storage locations (e.g., the badbitlines or bad columns may be different in number and/or located indifferent places amongst the different memory areas). Differentcodebooks may provide different decoding performance for the differentmemory areas due to the differing bad storage locations. As examples,encoding/decoding situations where a check node is connected to too manybad variable nodes or where too many bad variable nodes areparticipating in minimal or short cycles may lead to decodingperformance degradation, as described in further detail below. As such,if a single codebook is used to encode and decode data written and readfrom all of the memory areas, the decoding performance may be better forsome memory areas than others. Conversely, by utilizing multiplecodebooks optimally chosen for the different memory areas, overalldecoding from the memory dies 104 as a whole may be improved.

FIG. 8 below shows an example embodiment of components of the controller102, and FIGS. 9 and 10 show flow charts of codebook identification andevaluation processes that may be used by the components of FIG. 8, toevaluate and select the N codebooks 506(1)-506(N) based on decodingmetrics for the different memory areas. By analyzing decoding metrics toevaluate and select the N codebooks 506(1)-506(N), optimal codebooks maybe selected for the different memory areas with different bad storagelocations.

In further detail, FIG. 8 shows a block diagram of components of anexample embodiment of the controller 102 that may be involved incodebook evaluation and identification processes based on decodingmetrics to identify the N-number of codebooks 506(1)-506(N). For someexample configurations, the components other than the RAM 116 may becomponents of the ECC engine 124, although in other exampleconfigurations, some or all of these components may be consideredcomponents separate from the ECC engine 124. In addition to the RAM 116,the components involved in the codebook identification process mayinclude the parity bit generator module 502, a codebook selector module802 (which may be the same as or different than the codebook selectormodule 504 of FIG. 5), a codebook library 804, a read module 806, adecoder module 808, a decode evaluation module 810, a codebook scoringchart 812, and a memory area identification module 816.

In further detail, the codebook library 804 may store and/or include anM-number of codebooks 814(1)-814(M). The number M may be the same as orlarger than the number N. The M-number of codebooks 814(1)-814(M) mayrepresent the possible or available codebooks that the memory system 100may use for the N-number of codebooks 506(1)-506(N). In some exampleconfigurations, the codebook library 804 may be stored in memoryinternal to the memory system 100, although in other exampleconfigurations, the codebook library 804 may be stored external to thememory system 100, such as in an external device that may be connectedto memory system 100.

In some example configurations, one or more of the M codebooks814(1)-814(M) may be selected as one or more of the N codebooks506(1)-506(N) for the predetermined memory areas of the memory dies 104during a production phase. The memory area identification module 816 mayidentify a particular memory area for which a codebook from the codebooklibrary 804 is to be selected. For each memory area, each of the Mcodebooks 814(1)-814(M) may be evaluated and a best codebook of the Mcodebooks 814(1)-814(M) may be chosen for that memory area. Inparticular, for a given memory area identified by the memory areaidentification module 816, the codebook selection module 802 may cyclethrough the M codebooks 814(1)-814(M), and for each of the codebooks814(1)-814(M) it selects, the parity bit generator module 502 may usethe selected codebook to encode at least one information bit sequence togenerate an associated codeword. After the codeword is generated andprogrammed into the memory area, the read module 806 may issue a readcommand to the sequencer module 126, which in turn may issue one or moreread context commands to the memory dies 104 via the memory interface130 to have the codeword read out of the memory dies 104. In turn, thedecode module 808 may decode the read codeword using the selectedcodebook, and the decoded information bits may be loaded into the RAM116.

During the decoding process, the decode evaluation module 810 maydetermine a decoding metric for the decode process. An example decodemetric may include an amount of time that the decoder module 808 took tosuccessfully decode the data. Another decoding metric may be a number ofdecoding iterations that the decoder module 808 took to successfullydecode the data. Other decoding metrics may be possible. The decodeevaluation module 810 may record the evaluation results (e.g., thedecoding metric) in the codebook scoring chart 812. After all of the Mcodebooks 814(1)-814(M) have been cycled through, the codebook selectormodule 802 may evaluate the codebook scoring results to determine thebest codebook for that memory area. The best codebook may then be storedor otherwise identified in the codebook database 508 as one of the Ncodebooks 506(1)-506(N) to be used for encoding and decoding duringoperation of the memory system. The codebook identification process maybe performed for all of the memory areas within the memory dies 104.

Additionally, for some example codebook identification processes,multiple program and read operations may be performed on a given memoryarea using the same one of the M codebooks 814(1)-814(M) in order toobtain an average decoding metric for a given codebook for that memoryarea. For example, where the memory is a plane of a particular die, datamay be programmed into a certain percentage of the blocks in the planeusing the same codebook, and an average decoding metric may be obtainedby decoding the data stored in the certain percentage of the blocks. Inaddition or alternatively, multiple read and decoding operations may beperformed on the same data to generate an average decoding metric.Various configurations may be possible.

FIG. 9 shows a flow chart of an example method 900 of selecting the Ncodebooks 506(1)-506(N) from the M-number of codebooks 814(1)-814(M) inthe codebook library 804. At block 902, the memory area identificationmodule 816 identifies the next memory area in the dies 104. If theexample method 900 is just starting, then the next memory area may be aninitial memory area that the memory area identification module 816 isconfigured to identify. At block 904, the codebook selection module 802may select a next one of the M codebooks 814(1)-814(M) from the library804. At block 906, the parity bit generator module 502 may encode agiven bit sequence by generating parity bits for the given bit sequence.In some example methods, the given bit sequence may be a predeterminedsequence of bits generated for a production or testing phase. At block908, the sequencer module 126 programs a codeword including the givenbit sequence and the parity bits generated at block 906 into the memoryarea identified at block 902.

At block 910, the codeword may be read out of the memory area and thedecoder module 808 may decode the codeword using the codebook selectedat block 904. Additionally, at block 910, the decode evaluation module810 may determine a decoding metric (e.g., decoding time or number ofdecoding iterations) for the decoding process performed by the decodermodule 808. In some example methods, the codeword may be read severaltimes and/or the decoder module 808 may decode the codeword severaltimes to generate an average decoding metric for decoding thatparticular codeword with the codebook selected at block 904. Also, atblock 910, the decode evaluation module 810 may record the decodingmetric in the codebook scoring chart 812.

At block 912, if another codeword is to be programmed into the memoryarea, then the method 900 may proceed back to block 906, where anotherbit sequence may be encoded with the parity bits, the resulting codewordmay be programmed into the memory area at block 908, and decoding ofthat codeword with the codebook selected at block 904 may be evaluatedat block 910. Alternatively, at block 912, if another codeword is not tobe programmed into the memory area, then the method 900 may proceed toblock 914, where the codebook selector module 802 may determine whetherthere is another or next codebook in the codebook library 804 to beevaluated. If so, then the method 900 may proceed back to block 904, andthe codebook selector module 802 may select the next codebook from thecodebook library 804. If not, then at block 916, the codebook selectormodule 802 may evaluate the decoding metric results for the codebooksselected from the library 804 to encode and decode data programmed intoand read from memory area and select a best or optimal codebook for thatmemory area. For example, the codebook selector module 802 may selectthe codebook that yielded the shorted decoding or the fewest number ofiterations to successfully decode the data.

At block 918, the memory area identification module 816 may determinewhether there is another memory area of the memory dies 104 for which acodebook is to be identified or chosen. If so, then the method 900 mayproceed back to block 902, where the memory area identification module902 may identify a next memory area and the method 900 may repeat.Alternatively, if there are no more memory areas for which a codebook isto be identified, then the method 900 may end.

Referring back to FIG. 8, for some example configurations, the codebookselector module 802 may be configured to select a different codebook toencode a decode data for a particular memory area from the one it iscurrently using based on its normal operation of the memory system 100(e.g., after the production phase when it is reading and writing data inresponse to host commands). To illustrate, as part of read and writeoperations during normal operation, the ECC engine 124 may encode anddecode data for a particular memory area using one of the N codebooks506(1)-506(N), which may have been identified during a codebookidentification process of a production phase, as previously described.During a read operation, the read module 806 may request one or morecodewords to be read from the particular memory area, such as inresponse to a host read request. Prior to sending the requested databack to the host, the encoded data that is read may be decoded by thedecoder module 808. The decode evaluation module 810 may be configuredto monitor the decoding operations and determine decoding metrics forthe decoding operations. If the decode evaluation module 810 identifiesthat a decoding metric for a decoding operation has exceeded a threshold(e.g., a decoding time has exceeded a time threshold or a number ofdecoding iterations has exceeded an iteration threshold), the decodeevaluation module 810 may trigger the codebook selector module 802 todetermine if there is a better codebook available to use for the memoryarea for future read and write operations. In response, the componentsin FIG. 8 may perform a codebook identification process to determine ifthere is an available codebook that provides better decoding performancethan the one currently being used. The codebooks analyzed may be the Ncodebooks 506(1)-506(N) in the codebook database 508, the M codebooks814(1)-814(M) in the codebook library 804, or some combination thereof.

FIG. 10 is a flow chart of an example method 1000 of performing acodebook evaluation process for a particular memory area based on normaloperation of the memory system 100. At block 1002, the decode evaluationmodule 810 may determine to perform the codebook evaluation process inresponse to detection of a triggering event. The triggering event may bethat a threshold number of decode operations has exceeded a thresholdamount of decoding time, a threshold number of decode operations hasexceeded a threshold number of decoding iterations, or that an averagedecoding time or an average amount of decoding iterations to decode datafrom that memory area has exceeded a threshold. Other triggering eventsassociated with a decoding metric may be possible.

At block 1004, the codebook selector module 802 may determine if thereis storage space available within the memory area to read and write datafor evaluation of a new codebook for the memory area. To illustrate,suppose the memory area is a plane of one of the memory dies 104. Thecodebook selector module 802 may check if there are any free blockswithin that plane that it can use to perform the codebook evaluationprocess. If there is, then at block 1006, the codebook selector module802 may select an available codebook different from the one presentlyused to encode and decode data for the particular memory area. Theavailable codebook may be one of the N codebooks 506(1)-506(N) in thecodebook database 508 or one of the M codebooks 814(1)-814(M) in thecodebook library 804. At block 1008, the parity bit generator module 502may generate one or more sets of parity bits for one or more sets ofinformation bits to be encoded and stored in the available storage spacewithin the memory area, the resulting one or more codewords may bestored in the available storage space, the one or more codewords may bedecoded by the decoder module 808, and the decode evaluation module 810may monitor and record the decoding metrics of the decoding processes.

At block 1010, the codebook selector module 802 may determine if thecodebook selected at block 1006 provides better decoding metrics thanthe codebook currently used for the memory area, such as by comparingthe decoding metrics obtained at block 1008 with decoding metricspreviously obtained when writing and reading host data to the memoryarea. If so, then at block 1012, the codebook selector module 802 mayupdate the codebook database 508 to indicate that the new codebook is tobe used for future encoding and decoding for that memory area. If not,then at block 1014, the codebook selector module 802 may determine tocontinue to use the codebook that it was previously using for thatmemory area.

At block 1016, the codebook selector module 802 may determine if thereis another available codebook to evaluate. If so, then the method 1000may proceed back to block 1006, and the codebook selector module 802 mayselect a next codebook. The parity bit generator module 502 may thengenerate parity bits for additional information bits using the nextcodebook, and the decode evaluation module 810 may monitor and recordthe decoding metrics as the resulting codebooks are decoded by thedecoder module 808. Alternatively, at block 1016, if there is notanother available codebook, then the method may end.

Referring back to block 1004, if there is not currently any availablestorage space within the memory area to evaluate a new codebook for thememory area, then at block 1018 the codebook evaluation process may besuspended until storage space becomes available, such as if one or moreblocks are erased and become free. When that time happens and storagespace becomes available, then the method 1000 may proceed from block1018 to block 1006, and the codebook selector module 802 may select anavailable codebook for the codebook evaluation process for the memoryarea.

Instead of analyzing decoding metrics provided by different codebooks,other example embodiments of the memory system 100 may directly use thebad storage locations of the memory dies 104 to evaluate and scoreand/or rank the different codebooks for each of the memory areas. FIG.11 shows a block diagram of components of an example embodiment of thecontroller 102 that may be involved in codebook evaluation andidentification processes that may directly use bad storage locations ofa given memory area in order to score various codebooks for the givenmemory area. For some example configurations, the components may becomponents of the ECC engine 124, although in other exampleconfigurations, some or all of these components may be consideredcomponents separate from the ECC engine 124. The components may includea codebook scoring module 1102, a memory area identification module1104, a codebook library 1106 storing an M-number of codebooks1108(1)-1108(M) (which may be the same as or similar to the codebooklibrary 804 storing the M-number of codebooks 814(1)-814(M) of FIG. 8),and a bad storage database 1110, which may identify bad storagelocations for the various memory areas of the memory dies 104, aspreviously described.

In further detail, for a given memory area, the codebook scoring module1102 may be configured to assign a score to each of the M codebooks1108(1)-1108(M) in the library 1106. A score assigned to a particularcodebook may be based on a lifted graph structure associated with thecodebook. Reference is made to FIGS. 12A and 12B to describe liftedgraph structures in detail. FIG. 12A shows a schematic diagram of abipartite graph G of a LDPC code and FIG. 12B shows a schematic diagramof a corresponding lifted graph G′ of the LDPC code.

Referring to FIG. 12A, the bipartite graph G has set of six variablenodes v(1)-v(6) and a set of three check nodes v(1)-v(3). As shown,various edges connect the six variable nodes v(1)-v(6) with the threecheck nodes c(1)-c(3) in a particular configuration. Referring to FIG.12B, the corresponding lifted graph G′ has the same number of variablenodes (six) and the same number of check nodes (three). However, each ofthe variable nodes and each of the check nodes has a Z-number of layers.The lifted graph G′ shown in FIG. 12B has four layers (i.e., Z=4). Eachlayer of each variable node may be indicated by the term v(i,k), where iis an index from 1 to L that identifies the ith variable node (L beingthe number of variable nodes associated with the codebook), and k is anindex from 0 to Z−1 that identifies the kth layer of the ith variablenode. Similarly, each layer of each check node may be indicated by theterm c(n,q), where n is an index from 1 to K that identifies the nthcheck node (K being the number of check nodes associated with thecodebook), and q is an index from 0 to Z−1 that identifies the qth layerof the nth check node. FIG. 12B shows the first layers of the sixvariable nodes indicated by v(1,0), v(2,0), v(3,0), v(4,0), v(5,0), andv(6,0), and the first layers of each of the three check nodes indicatedby c(1,0), c(2,0), and c(3,0).

Layers of the variable nodes may be connected to the layers of the checknodes. An edge connecting a particular layer of a particular variablenode with a particular layer of a particular check node may be referredto as a Z-edge. Which of the variable node layers and check node layersthat each Z-edge is connected to may depend on the edge connections ofthe corresponding bipartite graph G and a shift value p. In particular,for a given edge in the bipartite graph G that connects a given ithvariable node v(i) with a given nth check node c(n), a corresponding setof Z-edges in the corresponding lifted graph G′ connects the ithvariable node layers v(i,0) to v(i,Z−1) with the nth check node layersc(n,0) to c(n,Z−1). For example, referring to FIG. 12A, an edge connectsthe first variable v(1) with the first check node c(1). Correspondingly,a set of four Z-edges connects the four layers of the first variablenode v(1,0) to v(1,3) with the four layers of the first check nodec(1,0) to c(1,3). Which variable node layer and which check node layerare connected together by a Z-edge may depend on the shift value passociated with the given set of Z-edges. The shift value p, which mayrange from 0 to Z−1, may indicate a number of check node layers a givenZ-edge is shifted relative to a variable node layer to which the givenZ-edge is connected. The shift is circular and may be a right-shift or aleft-shift. In the example lifted graph G′ of FIG. 12B, the shift is aright-shift and the shift value is 1 (i.e., p=1). As such, a set of fourZ-edges connecting the four layers of the first variable node v(1,0) tov(1,Z−1) with the four layers of the first check node c(1,0) to c(1,Z−1)may include a first edge connecting the first layer of the firstvariable node v(1,0) to the fourth layer of the first check node c(1,3),a second edge connecting the second layer of the first variable nodev(1,1) to the first layer of the first check node c(1,0), a third edgeconnecting the third layer of the first variable node v(1,2) to thesecond layer of the first check node c(1,1), and a fourth edgeconnecting the fourth layer of the first variable node v(1,3) to thethird layer of the first check node c(1,2). Other sets of Z-edges mayconnect various layers of the various variable nodes with various layersof the various check nodes accordingly. Additionally, each set ofZ-edges may have an associated shift value p, and the shift values maybe the same or different from one another.

Referring back to FIG. 11, the lifted attributes of a given codebook maybe used to determine a score for the codebook. In particular, each ofthe M codebooks 1108(1)-1108(M) may be in their lifted form or mayinclude associated lifted information. For example, each codebook 1108may include with it an associated number of layers Z and a shift value pfor each of the edges. The codebook scoring module 1102 may beconfigured to access each of the codebooks 1108(1)-1108(M) and calculatea corresponding score R_(CB(m)) for each mth codebook it accesses usingthe following mathematical equation:

$\begin{matrix}{R_{{CB}{(m)}} = {\sum\limits_{i = 1}^{L}{\sum\limits_{\underset{{connected}\mspace{14mu}{to}\mspace{11mu}{c{(j)}}}{j\mspace{11mu}{s.t.\;{v{(i)}}}\mspace{11mu}{is}}}^{\;}{\sum\limits_{q = 0}^{Z - 1}{\sum_{({d,\tau})}{{\hat{W}}_{({d,\tau})}^{v_{({i,0})}\rightarrow c_{({j,q})}}{{P_{CS}^{ɛ_{i}}\left( {\frac{\left( {d + 1} \right)Z}{2{{GCD}\left( {{q - p},Z} \right)}},\frac{\left( {\tau - 2} \right)Z}{{GCD}\left( {{q - p},Z} \right)}} \right)}.}}}}}}} & (3)\end{matrix}$For simplicity, the Ŵ term is referred to as the first scoring term, andthe P_(CS) ^(ε) ^(i) term is referred to as the second scoring term.Additionally, the four summations are referenced from right to left, orinner-most to outer-most, including a first summation Σ_((d,τ)), asecond summation

$\sum\limits_{q = 0}^{Z - 1},$a third summation

$\sum\limits_{\underset{{connected}\mspace{14mu}{to}\mspace{11mu}{c{(j)}}}{j\mspace{11mu}{s.t.\;{v{(i)}}}\mspace{11mu}{is}}}^{\;},$and a fourth summation

$\sum\limits_{i = 1}^{L}.$Calculation of the score R_(CB(m)) with reference to the summations isdescribed in further detail below. The following terms and definitionsare provided in order to describe in detail the scoring equation (3) andhow the first and second scoring terms may be calculated.

-   -   An extrinsic check node to a set of variable nodes is a check        node that is singly connected to the set of variable nodes.    -   An intrinsic check node to a set of variable nodes is a check        node that is connected to the set of variable nodes at least        twice.    -   An extrinsic message degree (EMD) of a set of variable nodes is        the number of extrinsic check nodes connected to the set of        variable nodes.    -   A set of variable nodes forms or participates in a cycle if        there exists a path passing through all of the variable nodes in        the set to itself without traversing an edge twice.    -   A set of variable nodes forms a minimal cycle if: (1) it forms a        cycle, and (2) no subset of the variable nodes forms a cycle.    -   A cycle set with the parameters (d,ω,τ) (otherwise referred to        as a (d,ω,τ) cycle set), is a set of d variable nodes that form        a minimal cycle and has ω intrinsic check nodes and τ extrinsic        check nodes.    -   For a given (d,ω,τ) cycle set, the number of intrinsic check        nodes ω is equal to d (ω=d). Accordingly, a (d,ω,τ) cycle set is        the same as a (d,d,τ) cycle set, which is denoted as a (d,τ)        cycle set.    -   A stopping set S is a subset of the set of variable nodes V        making up the bipartite graph such that no extrinsic check nodes        are connected to the stopping set S.    -   A set of variable nodes forms a minimal cycle with respect to an        edge e if: (1) it forms a cycle that contains the edge e,        and (2) no subset of the variable nodes forms a cycle that        contains the edge e.    -   A (d,ω,τ) e-cycle set is a set of d variable nodes that forms a        minimal cycle with respect to an edge e and has ω intrinsic        check nodes and τ extrinsic check nodes.        Calculation of the first and second scoring terms is now        described with reference to these defined terms.

The first scoring term, Ŵ_((d,τ)) ^(ν) ^((i,0)) ^(→c) ^((j,q)) , is thenumber of minimal paths from the first layer of the ith variable nodev(i,0) to the qth layer of the jth check node of length d and extrinsicmessage degree (EMD) τ.

The second scoring term, P_(CS) ^(ε) ^(i) (d,τ), denotes an upper boundon an expected contribution to a decoding error probability(alternatively referred to as a block error probability or decodingfailure probability) of a given (d,τ) cycle set, and the term P_(CS)^(ε) ^(i) (d,ω,τ) denotes an upper bound on an expected contribution toa decoding errory probability of a given (d,ω,τ) e-cycle set over binaryerasure channels with bit erasure probability ϵ_(i).

Accordingly, for a given ith variable node v(i) that is connected to agiven jth check node c(j), and for a particular qth layer of the jthcheck node, a first value may be calculated, the first value being theexpected contribution to a decoding error probability of a given (d,τ)cycle set, P_(CS) ^(ε) ^(i) (d,τ) (i.e., the second scoring term),multiplied by the number of minimal paths from the first layer of theith variable node v(i,0) to the qth layer of the jth check node oflength d and extrinsic message degree (EMD) τ, Ŵ_((d,τ)) ^(ν) ^((i,0))^(→c) ^((j,q)) (i.e., the first scoring term). As indicated by the firstsummation, the first scoring term, first values may determined for allpossible minimal cycles of length d and extrinsic message degree τ, andthe first values may be summed together to determine a second value. Inaddition, as indicated by the second summation, a second value may becalculated for each qth layer, from q=0 to Z−1, and the second valuesmay be summed together to generate a third value for the given ithvariable node v(i) connected to the given jth check node c(j). Inaddition, as indicated by the third summation, a third value may begenerated for each jth check node c(j) that is connected to the givenith variable node v(i), and the plurality of third values may be summedtogether to generate a fourth value. Further, as indicated by the fourthsummation, a fourth value may be generated for each ith variable nodev(i) for a given mth codebook, and the fourth values are summed togetherto generate the codebook scoring R_(CB(m)) for the given mth codebook.

Calculation of the first scoring term, Ŵ_((d,τ)) ^(ν) ^((i,0)) ^(→c)^((j,q)) , and the second scoring term, P_(CS) ^(ϵ)(d,τ), are nowdescribed in detail.

The first scoring term, Ŵ_((d,τ)) ^(ν) ^((i,0)) ^(→c) ^((j,q)) , iscalculated using an enumeration algorithm according to the followingterms:

-   -   The inputs to the enumeration algorithm are: (1) the lifted        graph G′ for which the first scoring term is being        calculated, (2) the index i for the ith variable node v_(i) for        which the first scoring term is being calculated, (3) a vector        of variable node degrees d _(ν) , corresponding to a degrees        spectrum Λ(x), which is defined as:        Λ(x)=Σ_(g=2) ^(d) ^(v) Λ_(g) x ^(g),  (4)    -   where Λ_(g) is the number of degree-g variable nodes, and d_(v)        is the maximal variable degree.    -   The output of the enumeration algorithm is a data structure W        containing for every possible check node c_(j), the spectrum of        minimal paths from the ith variable node v_(i) to the jth check        node c_(j), denoted as W(c_(j)).    -   D is a data structure that stores the depth of the graph G′        spanned from the ith variable node v_(i).    -   T_(ν) and T_(c) store the tiers of active variable nodes and        check nodes, respectively, at depth D. An active node n is a        node for which the path from the ith variable node v_(i) to node        n may lead to a minimal e-cycle set. T_(ν) ^(aprx) is a        temporary storage in the process of generating T_(ν).    -   Emd(n) and Emd^(D-2)(n) store the minimal EMD of a path from the        ith variable node v_(i) to node n among all paths from v_(i) to        node n up to tiers D and D−2, respectively.    -   Mult(ν_(i′)) and Mult(ν_(i′))^(D-2) store the multiplicity of        the minimal paths from the ith variable node v_(i) to the i'th        variable node v_(i′) at tiers D and D−2, respectively.    -   Parent(n) stores the parents of a node n in tier D along the        minimal paths from the ith variable node v_(i) to the node n.        For a set of nodes P, Parent(P) denotes the union set of all the        parents of nodes in P.    -   W(c_(j)) stores a set of triplets of the form (d,τ,m) for        logging the depth, EMD and multiplicity of minimal paths from        the ith variable node v_(i) to the jth check node c_(j), i.e.,        paths that may lead to a minimal e-cycle set of the edge e        connecting the ith variable node v_(i) to the jth check node        c_(j). The triplet (d,τ,m) means that there are in paths from        the ith variable node v_(i) to the jth check node c_(j) with        depth d and EMD τ.

Given these defined terms, the enumeration algorithm for calculating thefirst scoring term is calculated according to the following pseudocode:

W = CycleSetEnumerator(G′,i,d _(v)) % span a tree from v until there areno active variable nodes % and span for each visited check log thedepth, EMD and % multiplicity of all paths leading to a minimal e-cycleset % initialization Emd(v_(i)) ← d_(v) _(i) ; Mult(v_(i)) ← 1;Parent(v_(i)) ← Ø; ∀_(i′) ≠ i ∈ {1,..., N} Emd(v_(i′)) ← ∞; ∀_(j′)∈{1,..., M} Emd(v_(i′)) ← ∞; W(c_(j′)) ← Ø ; D ← 0; T_(v) ←{v_(i)} While(|T_(v)| ≠ 0) D ← D + 1 % Expand tier D of check nodes: T_(c) ←Ø for allv_(i′) ∈ T_(v) for all c_(j′) ∈ Neighbor(v_(i′),G′) \ Parent(v_(i′)) ifEmd(v_(i′)) < Emd(c_(j′)) % First length D minimal path from v_(i) toc_(j′) found Emd(c_(j′)) ← Emd(v_(i′)); Parent(c_(j′)) ←{v_(i′)};W(c_(j′)) ← W(c_(j′)) 

 (D, Emd(c_(j′)), Mult(v_(i′))); T_(c) ← T_(c)∪{c_(j′)}; else if(Emd(v_(i′)) = Emd(c_(j′))) & (c_(j′) ∈ T_(c)) % Another length Dminimal path from v_(i) to c_(j′) found Parent (c_(j′) ← Parent(c_(j′))∪ {v_(i′)}; (D,τ,m) ← {(d,τ,m) ∈ W (c_(j′)) | d = D}; W(c_(j′)) ←W(c_(j′)) 

 (D,τ,m + Mult(v_(i′))); end end end D ← D + 1 % Expand tier D ofvariable nodes: T_(v) ^(Aprx) ← Ø T_(v) ← Ø; ∀_(i′) ∈ {1,..., N}:Parent(v_(i′))← Ø  Emd^(D−2)(v_(i′)) ← Emd(v_(i′)); Mult^(D−2) (v_(i′))← Mult(v_(i′)); Mult(v_(i′)) ← 0; % Generate a list of possible activevariable nodes in tier D: for all c_(j′) ∈ T_(c) for all v_(i′) ∈Neighbor(c_(j′), G′) \ Parent(c_(j′)) Parent(v_(i′)) ← Parent(v_(i′)) ∪{c_(j′)}; T_(v) ^(Aprx) ← T_(v) ^(Aprx) ∪ {v_(i′)}; end end % Filter thelist leaving only true active variable nodes: for all v_(i′) ∈ T_(v)^(Aprx) P ← Parent(v_(i′)); for all v_(i″) ∈ Parent(P) S ← P ∩Neighbor(v_(i″),G′); if (Emd^(D−2)(v_(i) ″) + d_(v) _(i′) − 2|S| <Emd(v_(i′))) % First length D minimal path from v_(i) to v_(i′) foundEmd(v_(i′)) ← Emd^(D−2)(v_(i″)) + d_(v) _(i′) − 2|S|; Mult(v_(i′))←Mult^(D−2)(v_(i″)); Parent(v_(i′))← S; T_(v) ← T_(v) ∪ {v_(i′)}; else if(Emd^(D−2)(v_(i″)) + d_(v) _(i′) − 2|S| = Emd(v_(i′))) & (v_(i) ∈ T_(v))% Another length D minimal path from v_(i) to v_(i′) found Mult(v_(i′))← Mult(v_(i′)) + Mult^(D−2)(v_(i″)); Parent(v_(i′)) ← Parent(v_(i′)) ∪S; end end end end

As previously described, the enumeration algorithm may generate a datastructure W(c_(j)) for each jth check node connected to an ith variablenode, where the data structure W(c_(j)) includes and/or identifies mpaths from the ith variable node v_(i) to the jth check node c_(j) withdepth d and EMD τ. Accordingly, for an ith variable node connected to ajth check node, the codebook scoring module 1102 may identify the valueof the m paths. Where the ith variable node is connected to more thanone check node, the codebook scoring module 1102 may identify the valueof m paths for each of the check nodes that are connected to the ithvariable node, and sum the values together in order to determine thefirst scoring term Ŵ_((d,τ)) ^(ν) ^((i,0)) ^(→c) ^((j,q)) .

The second scoring term P_(CS) ^(ε) ^(i) (d,τ) can be calculatedaccording to the following equations (5)-(13) as follows:

$\begin{matrix}{{{P_{CS}^{ɛ_{i}}\left( {d,\tau} \right)} = {\sum\limits_{S = d}^{N}{{N_{S}\left( {d,d,\tau} \right)}ɛ_{i}^{S}}}},} & (5)\end{matrix}$where N is the cardinality of variable nodes, N_(s)(d,d,τ) is theexpected number of stopping sets of size S that contain the give (d,d,τ)cycle set, and ϵ_(i) is the bit erasure probability associated with agiven ith variable node v(i). The term N_(s)(d,d,τ) is computedaccording to the following equation:

$\begin{matrix}{{{N_{S}\left( {d,d,\tau} \right)} = {\sum\limits_{\rho = \tau}^{{Md}_{c} - {2d} - \tau}{{A\left( {{s - d},\rho} \right)} \cdot {B\left( {\rho,d,\tau} \right)}}}},} & (6)\end{matrix}$where d_(c) is the maximal check node degree, where A(s−d,ρ) is thenumber of subsets of variable nodes of size s-d emanating ρ edges, andwhere B(ρ,d,τ) is the probability that ρ edges form a stopping set overthe set of M check nodes from which d check nodes are the intrinsiccheck nodes of the given cycle set and τ check nodes are the extrinsiccheck nodes of the given cycle set. The term A(s−d,ρ) is computedaccording to the following generator polynomial:

$\begin{matrix}{{{A\left( {{s - d},\rho} \right)} = {{coeff}\left( {{\prod\limits_{i}\left( {1 + {yx}^{i}} \right)},{y^{s - d}x^{\rho}}} \right)}},} & (7)\end{matrix}$and the term B(ρ,d,τ) is computed according to the following equation:

$\begin{matrix}{{B\left( {\rho,d,\tau} \right)} = {\frac{\sum\limits_{i = \tau}^{\min{\{{\rho,{\tau{({d_{c} - 1})}}}\}}}{\sum\limits_{j = 0}^{\min{\{{{\rho - i},{d{({d_{c} - 2})}}}\}}}{{\alpha\left( {i,\tau} \right)}{\beta\left( {j,d} \right)}{\gamma\left( {{M - d - \tau},{\rho - i - j}} \right)}}}}{\begin{pmatrix}{{Md}_{c} - {2d} - \tau} \\\rho\end{pmatrix}}.}} & (8)\end{matrix}$The term α(i,τ) is the number of possibilities for connecting i edges tothe τ extrinsic check nodes such that each extrinsic check node isconnected at least once, and is computed according to the followingequation:α(i,τ)=coeff(((1+x)^(d) ^(c) ⁻¹−1)^(τ) ,x ^(i)).  (9)In addition, the term β(j,d) provides the number of possibilities forconnecting j edges to the d intrinsic check nodes, and is computedaccording to the following equation:

$\begin{matrix}{{\beta\left( {j,d} \right)} = {\begin{pmatrix}{\left( {d_{c} - 2} \right)d} \\j\end{pmatrix}.}} & (10)\end{matrix}$Further, the term γ(M−d−τ,ρ−i−j) provides the number of possibilitiesfor connecting the remaining (ρ−i−j) edges to the remaining (M−d−τ)check nodes such that a check node is either unconnected, or connectedat least twice, where M is the cardinality of the check nodes, and iscomputed according to the following equation:γ(M,ρ)=coeff(((1+x)^(d) ^(c) −d _(c) x)^(M) ,x ^(ρ)),  (11)In addition or alternatively, the following recursions are used togenerate pre-computed tables of α(i,τ) and γ(M,ρ) for all values of i,τ, M and ρ:

$\begin{matrix}{{{{\alpha\left( {i,\tau} \right)} = {\sum\limits_{j = 1}^{\min{\{{i,{d_{c} - 1}}\}}}{\begin{pmatrix}{d_{c} - 1} \\j\end{pmatrix}{\alpha\left( {{i - j},{\tau - 1}} \right)}}}},{where}}\left\{ \begin{matrix}{{\alpha\left( {i,0} \right)} = 1} & {{{if}\mspace{14mu} i} = 0} \\{{\alpha\left( {i,0} \right)} = 0} & {otherwise}\end{matrix} \right.} & (12) \\{and} & \; \\{{\gamma\left( {M,\rho} \right)} = {{\gamma\left( {{M - 1},\rho} \right)} + {\sum\limits_{j = 2}^{\min{\{{d_{c},\rho}\}}}{{\gamma\left( {{M - 1},{\rho - j}} \right)}\begin{pmatrix}d_{c} \\j\end{pmatrix}}}}} & (13) \\{where} & \; \\\left\{ \begin{matrix}{{\gamma\left( {0,\rho} \right)} = 1} & {{{if}\mspace{14mu}\rho} = 0} \\{{\gamma\left( {0,\rho} \right)} = 0} & {otherwise}\end{matrix} \right. & \;\end{matrix}$

Referring back to equation (3), the terms

$\frac{\left( {d + 1} \right)Z}{2{{GCD}\left( {{q - p},Z} \right)}}\mspace{14mu}{and}\mspace{14mu}\frac{\left( {\tau - 2} \right)Z}{{GCD}\left( {{q - p},Z} \right)}$can be substituted in for d and τ in equations (5)-(13) as appropriate,where GCD refers to “greatest common denominator.”

Additionally, referring back to equation (5), the second scoring termP_(CS) ^(ε) ^(i) (d,τ) may be calculated based on an ith bit erasureprobability ϵ_(i) associated with a given ith variable node v(i). Inthis context, a channel between the controller 102 and the memory dies104 may be considered and/or modeled after a binary erasure channel(BEC), where a transmitter sends an ith bit (at a value of 0 or 1) overthe channel to a receiver. The bit erasure probability ϵ_(i) is theprobability that the ith bit is received with zero or no reliability(i.e., that the receiver has no reliability or confidence that the bitvalue of the ith bit is correct). Accordingly, the quantity (1−ϵ_(i)) isthe probability that the ith bit is received with absolute reliability(i.e., that the receiver has absolute reliability or confidence that thebit value of the ith bit is correct).

As shown in equation (5), each ith bit erasure probability ϵ_(i) may beassociated with corresponding ith variable node, as indicated by thesubscript i. The value for the ith bit erasure probability ϵ_(i) may bedepend on whether the variable node with which it is associated isassociated with a good storage location or a bad storage location. Aspreviously described, the number of variable nodes may be equal to thenumber of bits of a codeword to be stored in a segment of storage. Sinceeach variable node corresponds to a particular bit of the codeword bitsequence, and each bit is stored in a particular memory cell of thesegment of storage, then for a given codeword, each associated variablenode is, in turn, associated with a particular memory cell of thesegment of storage where that codeword is stored. Otherwise stated, amemory mapping may map a given variable node to a given memory cell,which may be either a good memory cell or a bad memory cell.

Accordingly, when the codebook scoring module 1102 is cycling throughthe variable nodes to calculate the second scoring term, the codebookscoring module 1102 may access the bad storage location database 1110 todetermine whether a particular ith variable node is associated with agood memory cell or a bad memory cell. As used herein, a variable nodeassociated with a good memory cell may be referred to as a good variablenode, and a variable node associated with the bad memory cell may bereferred to as a bad variable node. If the codebook scoring module 1102determines that the ith variable node is associated with a good memorycell, then the codebook scoring module 1102 may assign a first value forthe associated ith bit erasure probability ϵ_(i). Alternatively, if thecodebook scoring module 1102 determines that the ith variable node isassociated with a bad memory cell, then the codebook scoring module 1102may assign a second value for the associated ith bit erasure probabilityϵ_(i). In a particular example configuration, the second value when theassociated memory cell is bad may be higher than the first value whenthe associated memory cell is good. For example, the first value may be0.2 and the second value may be 0.5. These values are merely exemplary,and other values may be used. Also, more than two different values maybe possible, particularly for configurations where more than two levels(good/bad) are used to assess the reliability of storage locations.

In sum, the codebook scoring module 1102 may use different erasureprobability values to calculate the expected contributions to a decodingerror probability of one or more cycle sets (i.e., the second scoringterm) for different variable nodes, and which erasure probability valuesthe codebook scoring module 1102 uses for each the expected contributioncalculations may depend on whether the corresponding variable nodes areassociated with good storage locations or bad storage locations. In aparticular configuration, for an expected contribution calculation, thecodebook scoring module 1102 uses a higher erasure probability valuewhen the corresponding variable node is associated with a bad storagelocation, compared to when the corresponding variable node is associatedwith a good storage location.

FIG. 13 shows a flow chart of an example method 1300 of a calculating acodebook score R_(CB(m)) for an mth codebook from the codebook library1106 for a given memory area. At block 1302, the codebook scoring module1102 may identify a next ith variable node of the mth codebook for whichto generate a scoring value. If the method 1300 is just starting, thenext ith variable node may be the first variable node v(1). At block1304, the codebook scoring module 1102 may determine whether the ithvariable node is associated with a good storage location or a badstorage location of the memory area. At block 1306, the codebook scoringmodule 1102 may calculate a scoring value for the ith variable node,such as by calculating a first value for the first scoring termŴ_((d,τ)) ^(ν) ^((i,0)) ^(→c) ^((j,q)) and a second value of the secondscoring term P_(CS) ^(ε) ^(i) for the ith variable node, and multiplyingthe terms together. The codebook scoring module 1102 may calculate thefirst scoring term Ŵ_((d,τ)) ^(ν) ^((i,0)) ^(→c) ^((j,q)) using theenumeration algorithm, and may calculate the second scoring term P_(CS)^(ε) ^(i) using equations (5)-(13), as previously described. Whencalculating the second scoring term P_(CS) ^(ε) ^(i) , the codebookscoring module 1102 may select or set a value for the bit erasureprobability ϵ_(i) based on whether the ith variable node is associatedwith a bad memory cell or a good memory cell. As previously described,the erasure probability value may be higher if the ith variable node isassociated with a bad memory cell compared to if it is associated with agood memory cell.

At block 1308, the codebook scoring module 1102 may determine whetherthere is another or next variable node for which to calculate a score(or scoring value). If so, then the method 1300 may proceed to the nextith variable node at block 1302. If not, then at block 1310, thecodebook scoring module 1102 may determine a codebook score R_(CB(m))for the mth codebook based on the scores (or scoring values) determinedfor each of the ith variable nodes of the mth codebook. In a particularexample, the codebook scoring module 1102 may sum the scoring valuestogether to generate the codebook score R_(CB(m)) for the given memoryarea.

FIG. 14 is a flow chart of an example method 1400 of selecting acodebook from a plurality of codebooks for each of a plurality of memoryareas of the memory dies 104. At block 1402, the memory areaidentification module 1108 may identify a next memory area of theplurality of memory dies 104 for which to select a best codebook fromthe codebook library 1106. If the method 1400 is in its initialiteration, the next memory area may be an initial memory area that thememory area identification module 1108 is configured to select. At block1404, the codebook scoring module 1102 may select a next mth codebookfrom the codebook library 1106. The next mth codebook may be an initialcodebook where the codebook is the first codebook selected for thememory area.

At block 1406, the codebook scoring module 1102 may calculate a codebookscore R_(CB(m)) for the mth codebook that is selected at block 1404. Thecodebook score R_(CB(m)) may be calculated in accordance with the method1300 of FIG. 13, as previously described. At block 1408, the codebookscoring module 1102 may determine whether there is another codebook inthe codebook library 1106 to score for the memory area identified atblock 1402. If there is, then the method 1400 may proceed back to block1404, where the codebook scoring module 1102 selects a next codebook toscore from the library 1106. Alternatively, if there are no furthercodebooks to score for the memory area, then the method 1400 may proceedto block 1410, where the codebook scoring module 1102 selects a bestcodebook from the library 1106 to use for encoding and decoding for thememory area. The codebook scoring module 1102 may determine or selectthe best codebook based on which of the codebooks yielded the highestscore, as calculated at block 1406. After making the selection, thecodebook scoring module 1102 may identify the best codebook for thememory area as one of the N codebooks 506(1)-506(N) in the codebookdatabase 508.

At block 1412, the memory area identification module 1108 may determineif there is another memory area of the memory dies 104 for which toselect a best codebook from the codebook library 1106. If there is, thenthe method 1400 may proceed back to block 1402, where the memory areaidentification module 1102 identifies a next memory area. If not, thenthe method 1400 may end.

As previously described, the codebook scoring module 1102, the memoryarea identification module 1104, and the bad storage database 1110 maybe components of the memory system 100, such as components of the ECCengine 124 or another components of the controller 102. In anotherexample embodiment, the codebook scoring module 1102, the memory areaidentification module 1104, and the bad storage database 1110 may becomponents of a controller of an external computing device or system,such as a testing device or system, that is external to the memorysystem 100. The external computing device may have access to and/or havestored therein the codebook library 1106. Based on the bad storagelocations of the memory areas, the codebook scoring module 1102 and thememory area identification module 1104, may operate to analyze the Mcodebooks 1108(1)-1108(M) stored in the codebook library 1106 to selectthe best codebooks for each of the memory areas of the memory dies 104,such as by performing the example methods of 1300 and 1400 of FIGS. 13and 14 respectively. The external computing device may then load theselected best codebooks into the codebook database 508 of the memorysystem 100 as the N-number of codebooks 506(1)-506(N) that the ECCengine 124 uses to encode and decode data for the various memory areasof the memory dies 104.

In other example embodiments, some of the components shown in FIG. 11may be components of the memory system 100 and the other of thecomponents may be components of a controller of the external computingdevice or system. Which components are part of the memory system 100 andwhich are part of the external computing device or system may vary. Forthese embodiments, the components of the memory system 100 and thecomponents of the external computing device or system may communicatewith each other in order to ultimately have the selected best codebooksloaded into the codebook database 508 of the memory system 100. Variousways of integrating the components shown in FIG. 11 into the memorysystem 100, an external computing device or system, or a combinationthereof, may be possible.

In other example embodiments, instead of evaluating a plurality ofcodebooks from a library based on decoding metrics (as described withreference to FIGS. 8-10), or using a scoring algorithm (as describedwith reference to FIGS. 11-14), the memory system 100 may be configuredto determine a codebook for a particular memory area by modifying orpermuting an existing codebook based on bad storage locations of theparticular memory area. FIG. 15 shows a block diagram of components ofan example embodiment of the controller 102 that may be involved in acodebook modification or permuting process to generate modified orpermuted codebooks based on bad storage locations for memory areas ofthe memory dies 104. For some example configurations, the components maybe components of the ECC engine 124, although in other exampleconfigurations, some or all of these components may be consideredcomponents separate from the ECC engine 124. The components involved mayinclude a codebook modification module 1502, a memory areaidentification module 1504, a bad storage database 1506, which mayidentify bad storage locations for the various memory areas of thememory dies 104 as previously described, and the codebook database 508,which may store and/or include an initial or common codebook 1506 and anN-number of modified codebooks 1508(1) to 1508(N) to encode and decodedata for the plurality of memory areas for the plurality of memory dies104.

In some example embodiments, the initial codebook 1506 may be loadedinto the codebook database 508 during the life of the memory system 100,such as during production of the memory system 100. Although FIG. 15shows one initial codebook 1506, more than one initial codebook 1506 maybe loaded into the codebook database 508 in other exampleconfigurations. In general, the initial codebook 1506 may be a codebookhaving a particular configuration that is not based on any bad storagelocations of the memory dies 104. At least one of the modified codebooks1508(1)-1508(N) may be a modification or permutation of the initialcodebook 1506, and the other of the modified codebooks 1508(1)-1508(N)may each be a modification or permutation of the initial codebook 1506or another modified or permuted codebook.

In one example configuration of codebook modification, the codebookmodification module 1502 may be configured to modify one of thecodebooks to generate a modified codebook based on numbers of variablenodes associated with bad storage locations connected to check nodes. Inparticular, the existing codebook may be modified by reducing the numberof connections that certain check nodes have to variable nodesassociated with bad storage locations. The notion is that decodingperformance for a given memory area may be less than optimal if thecodebook used to encode and decode data stored in the given memory areahas one or more check nodes that are connected to too many variablenodes associated with bad storage locations. By identifying these checknodes and generating a modified codebook by reducing the number ofconnections these check nodes have to variable nodes associated with badstorage locations, decoding performance for the given memory area may beimproved.

In further detail, when the codebook modification module 1502 is todetermine a codebook for a particular memory area, the codebookmodification module 1502 may select an existing codebook in the codebookdatabase 508 (either the initial codebook 1506 or modified codebook 1508that the codebook modification module 1502 generated for another memoryarea) and may determine the bad storage locations for the particularmemory area, such as by accessing the bad storage database 1506. Basedon identifying the bad storage locations, the codebook modificationmodule 1502 may be configured to determine which of the variable nodesof the existing codebook are associated with the bad storage locationsof the particular memory area.

As used herein, a connection (or edge) that connects a check node with agood variable node may be referred to as a good connection (or goodedge), and a connection (or edge) that connects a check node with a badvariable node may be referred to as a bad connection (or bad edge). Upondetermining which of the variable nodes are associated with the badstorage locations of the particular memory area, the codebookmodification module 1502 may be configured to traverse the check nodesof the existing codebook, and for each check node, count the number ofbad variable nodes or bad edges connected to that check node.

In the event that the codebook modification module 1502 determines togenerate a modified codebook based on an existing codebook, the codebookmodification module 1502 may use the count information to determine howto modify the existing codebook. In a particular example configuration,the codebook modification module 1502 may use the count information toidentify one or more candidate check nodes that may be the subject ofthe codebook modification. The codebook modification module 1502 maythen select one or more of the candidate check nodes to be the subjectof the codebook modification. In turn, the codebook modification module1502 may be configured to modify the existing codebook by reducing thenumber of bad edges connected to the candidate check nodes that itselects.

The codebook modification module 1502 may identify the candidate checknodes in various ways. In one example configuration, the codebookmodification module 1502 may utilize a count threshold. If the number ofbad variable nodes or bad edges connected to a given check node exceedsthe count threshold, then the codebook modification module 1502 may beconfigured to identify the given check node as a candidate check node.In some example configurations, the count threshold may be one, althoughother numbers may be possible. In addition or alternatively to using acount threshold, the codebook modification module 1502 may utilize acount range to identify the check node as a candidate check node. Thatis, if the number of bad variable nodes or bad edges is within the countrange, then the codebook modification module 1502 may be configured toidentify the given check node as a candidate check node. For anotherexample configuration, the codebook modification module 1502 maydetermine a predetermined number of check nodes that are connected tothe highest number of bad variables. The codebook modification module1502 may identify those check nodes as candidate check nodes. So, forexample, if the predetermined number is 5, then the codebookmodification module 1502 may be configured to identify the five checknodes that are connected to the most bad variable nodes, and identifythose five check nodes as candidate check nodes. Other ways ofidentifying candidate check nodes for codebook modification based on thecount information may be possible.

Upon identifying one or more candidate check nodes, the codebookmodification module 1502 may be configured to modify or permute theexisting codebook by reducing the number of bad connections to one ormore of the candidate check nodes. The codebook modification module 1502may modify the existing codebook by reducing the number of badconnections for only some of the candidate check nodes, or for all ofthe candidate check nodes.

The codebook modification module 1502 may be configured to modify anexisting codebook through a reduction of the number of bad connectionsto selected candidate check nodes in various ways. For a given selectedcandidate check node, the codebook modification module 1502 may modify acodebook by removing one or more bad connections connected to theselected check node from the codebook; switching one or more badconnections connected to the selected check node to be connected to oneor more non-candidate check nodes; swapping one or more bad connectionswith one or more good connections so that the total number of edgesconnected to the candidate and non-candidate check nodes remains thesame, or some combination thereof. In addition or alternatively, thecodebook modification module 1502 may modify a codebook by swapping twoor more columns of an associated parity-check matrix with each other.One of the columns involved in the swapping may correspond to a badvariable node connected to the selected check node, and another of thecolumns involved in the swapping may correspond to a good variable nodeunconnected with the selected check node.

To illustrate an example codebook modification based on numbers of badedges connected to check nodes, FIG. 16A shows a Tanner graph of anexisting codebook that may be included in the codebook database 508. TheTanner graph in FIG. 16A indicates that the existing codebook includestwelve variable nodes v(1) to v(12) and four check nodes c(1) to c(4).As shown in FIG. 16A, an edge connects the first variable v(1) with thefirst check node c(1), an edge connects the first variable v(1) with thesecond check node c(2), and so on. Additionally, FIG. 16A shows storagelocations of the memory area with which each variable node isassociated. For example, the first variable node v(1) is associated withthe first storage location, the second variable node v(2) is associatedwith the second storage location, and so on. For configurations wherethe memory area is a plane, the storage locations indicated in FIG. 16Amay be bit lines. For configurations where the memory area is a segmentof storage, the storage locations may be memory cells.

Suppose, for example, that of the twelve storage locations, the badstorage locations are the second, seventh, and twelfth storagelocations, as indicated by the bolded boxes around those storagelocations. Accordingly, the first check node c(1) is connected to onebad variable, v(7); the second check node c(2) is connected to three badvariables, v(2), v(7), and v(12); the third check node c(3) is connectedto two bad variables, v(2) and v(12); and the fourth check node c(4) isconnected to two bad variables, v(7) and v(12).

In the event that the codebook modification module 1502 wants to modifythe existing codebook shown in FIG. 16A, the codebook modificationmodule 1502 may identify the second check node c(2) as a candidate checknode. In one example, the bad connection or bad variable threshold usedby the codebook modification module 1502 may be two, and the codebookmodification module 1502 may identify the second check node c(2) as acandidate check node since the number of bad connections connected tothe second check node c(2) (three) is greater than the bad connectionthreshold. As another example, the codebook modification module 1502 mayidentify the second check node c(2) as a candidate check node because ithas the highest number of bad connections connected to it among the fourcheck nodes c(1) to c(4).

Upon identifying the second check node c(2) as a candidate check node,the codebook modification module 1502 may modify the existing codebookby reducing the number of bad connections connected to the second checknode c(2). In one example, the codebook modification module 1502 mayreduce the number of bad connections connected to the second check nodec(2) by removing one or more of the bad connections from the codebook.For example, one of the bad connections of the existing codebookconnects the second variable v(2) to the second check node c(2). Thecodebook modification module 1502 may modify the existing codebook byremoving that bad connection from the codebook.

As another example modification, the codebook modification module 1502may modify the existing codebook by moving the bad connection connectingthe second variable node v(2) to the second check node c(2) so that thebad connection connects the second variable node v(2) to a non-candidatecheck node, such as the first check node c(1). This moving of the badconnection is indicated in FIG. 16B by the bolded connection connectingthe second variable node v(2) to the first check node c(1). In thisexample, the number of bad connections connected to the second checknode c(2) is reduced by one, while the number of bad connectionsconnected to the first check node c(1) is increased by one. For someexample configurations, as illustrated in FIG. 16B, the bad connectionis moved to a check node having the lowest or one of the lowest numberof bad connections, which in this case is the first check node c(1). Aspreviously described, both the third and fourth check nodes c(3), c(4)have two bad connections, and adding another bad connection to either ofthese check nodes c(3), c(4) may be undesirable since doing so wouldyield a codebook modification with a check node having three badconnections.

As another example modification, the codebook modification module 1502may modify the existing codebook by swapping a bad connection connectedto the second check node c(2) with a good connection connected toanother check node. For example, as depicted in FIG. 16B, in addition tomoving the bad connection connected to the second variable node v(2)from the second check node c(2) so that it is instead connected to thefirst check node c(1), a good connection connecting the first check nodec(1) with a good variable node may be moved so that the good connectionis connected to the second check node c(2). For example, as shown inFIGS. 16A and 16B, a good connection connected to the fifth variablenode v(5) may be moved from being connected to the first check node c(1)to the second check node c(2). In this latter example, the number of badconnections connected to the second check node c(2) is reduced by one,while the overall number of connections connected to each of the checknodes has remained the same.

For simplicity, the example codebook modification illustrated in FIGS.16A and 16B shows reducing the number of bad connections for only onecheck node and by reducing the number of bad connections by one. Inother example configurations, the number of bad connections may bereduced for more than one check node and/or more than one bad connectionmay be removed from a given candidate check node. Also, in the examplecodebook modification illustrated in FIGS. 16A and 16B, the check nodeidentified as a candidate check node (i.e., the second check node) wasalso the check node selected to be the subject of the codebookmodification. In other example configurations, as mentioned, there maybe more than one check node identified as a candidate, but less than allof the candidate nodes are selected for modification. Variousconfigurations for selecting check nodes for codebook modification basedon numbers of bad connections may be possible.

In another example configuration of codebook modification, the codebookmodification module 1502 may be configured to modify one of thecodebooks to generate a modified codebook based on numbers of badvariable nodes participating in minimal cycles. The notion is thatdecoding performance for a given memory area may be less than optimal ifthe codebook used to encode and decode data stored in the given memoryarea has too many bad variable nodes participating in minimal cycles. Byidentifying these bad variable nodes and generating a modified codebookthat has reduced the number of bad variable nodes participating in oneor more minimal cycles, decoding performance for the given memory areamay be improved.

As previously described, a set of variable nodes forms or participatesin a cycle if there exists a path passing through all of the variablesin the set to itself without traversing an edge twice, and the set ofvariable nodes forms a minimal cycle if: (1) it forms a cycle, and (2)no subset of the variable nodes forms a cycle.

For a given codebook selected from the codebook database 508, thecodebook modification module 1502 may be provided with or otherwisedetermine the various minimal cycles and particular variable nodesparticipating in the various minimal cycles for the given codebook.Additionally, the codebook modification module 1502 may be configured todetermine which of the variable nodes participating in the minimalcycles are bad variable nodes, such as by accessing the bad storagedatabase to determine the variable nodes associated with bad storagelocations for a given memory area. Based on this information, thecodebook modification module 1502 may be configured to determine thenumber of bad variable nodes that are participating in each of theminimal cycles of the selected codebook.

In the event that the codebook modification module 1502 determines togenerate a modified codebook based on an existing codebook, the codebookmodification module 1502 may use the information identifying the badvariables participating in the minimal cycles and/or the numbers of badvariables participating in the minimal cycles to determine how to modifythe existing codebook. In a particular example configuration, thecodebook modification module 1502 may use the information to identifyone or more candidate minimal cycles that may be the subject of thecodebook modification. The codebook modification module 1502 may thenselect one or more of the candidate minimal cycles to be the subject ofthe codebook modification. In turn, codebook modification module 102 maybe configured to modify the existing codebook by reducing the number ofbad variables participating in the minimal cycles that it selects.

The codebook modification module 1502 may identify the candidate minimalcycles in various ways. In one example configuration, the codebookmodification module 1502 may utilize a count threshold. If the number ofbad variable nodes participating in a given minimal cycle exceeds thecount threshold, then the codebook modification module 1502 may beconfigured to identify the minimal cycle as a candidate minimal cycle.

For other example configurations, the codebook modification module 1502may utilize a threshold based on a length of the minimal cycle and thenumber of bad variables participating in the minimal cycles. In aparticular example configuration, the threshold may be a differencethreshold corresponding to a difference between a length of the minimalcycle and the number of bad variables participating in the minimalcycle. In general, the length of a cycle may be equal to the number ofedges of the cycle. Of the various minimal cycles of a codebook, any twominimal cycles may have the same length or differing lengths. For agiven minimal cycle, the codebook modification module 1502 may beconfigured to determine a difference between the length of the minimalcycle and the number of bad variable nodes participating in the minimalcycle. If the difference is below the difference threshold, then thecodebook modification module 1502 may be configured to identify theminimal cycle as a candidate minimal cycle. In another particularexample configuration, the threshold may correspond to a ratio of thenumber of bad variables participating in the minimal cycle to the lengthof the minimal cycle. Other types of threshold values that consider boththe length of the minimal cycle and the number of bad variable nodesparticipating in the minimal cycle may be possible.

For other example configurations, the codebook modification module 1502may utilize a threshold based on the number of bad variables and thetotal number of variables participating in the minimal cycles. In aparticular example configuration, the threshold may be a differencethreshold corresponding to a difference between the total number ofvariables participating in the minimal cycle and the number of badvariables participating in the minimal cycle. If the difference is belowthe difference threshold, then the codebook modification module 1502 maybe configured to identify the minimal cycle as a candidate minimalcycle. In another particular example configuration, the threshold maycorrespond to a ratio of the number of bad variables participating inthe minimal cycle to the total number of variables participating in theminimal cycle. Other types of threshold values that consider both thenumber of bad variable nodes and the total number of variable nodesparticipating in the minimal cycle may be possible. For example, athreshold value may be based on the length of minimal cycle, the numberof bad variable nodes participating in the variable cycle, and the totalnumber of variable nodes participating in the variable cycle.

For still other example configurations, the codebook modification module1502 may be configured to determine a predetermined number of minimalcycles with the largest number of participating bad variables, apredetermined number of minimal cycles with the smallest differencebetween the cycle length and the number of participating bad variables,a predetermine number of minimal cycles having the largest ratio of badvariables to minimal cycle length, a predetermined number of minimalcycles with the smallest difference between the number of participatingbad variables and the total number of participating variables, or apredetermined number of minimal cycles having the largest ratio ofparticipating bad variables to total participating variables.

Other ways of identifying candidate minimal cycles for codebookmodification based on numbers of bad variables participating in theminimal cycles may be possible. For example, in addition oralternatively to utilizing a threshold, the codebook modification module1502 may utilize a range, and may determine a minimal cycle to be acandidate minimal cycle based on a determined value relative to therange.

Upon identifying one or more candidate minimal cycles, the codebookmodification module 1502 may be configured to modify or permute theexisting codebook by reducing the number of bad variable nodesparticipating in one or more of the candidate minimal cycles. Thecodebook modification module 1502 may modify the existing codebook byreducing the number of bad variable nodes for only some of the candidateminimal cycles, or for all of the candidate minimal cycles. The effectof the modification is that minimal cycles that are selected forcodebook modification may be removed or broken up and, in at least somesituations, a new minimal cycle may be formed, where the newly formedminimal cycle has a fewer number of participating bad variable nodes, alarger difference between the length of the newly formed minimal cycleand the number of participating bad variable nodes, a smaller ratio ofthe number of participating bad variable nodes to the minimal cyclelength, a larger difference between the total number of participatingvariable nodes and the number of participating bad variable nodes, asmaller ratio of the number of participating bad variable nodes to thetotal number of participating variable nodes, or some combinationthereof.

The codebook modification module 1502 may be configured to modify anexisting codebook through a reduction in the number of bad variablesparticipating in a selected minimal cycle in various ways. For a givenselected candidate minimal cycle, the codebook modification module 1502may modify a codebook by removing one or more connections connected toone or more bad variable nodes participating in the selected minimalcycle from the codebook; switching one or more connections connected toone or more bad variable nodes of the selected minimal cycle to beconnected to one or more different check nodes (i.e., for a given edge,keeping the bad variable node the same but changing the check node towhich the edge is connected to a different check node); changing a badconnection to a good connection (i.e., for a given edge, keeping thecheck node the same but changing the variable node to which the edge isconnected from the bad variable node participating in the minimal cycleto a good variable node); or some combination thereof. Additionally, forsome modifications involving the switching or the changing, acorresponding connection change may be made so that the overall numberof edges connected to each of the variable nodes and the overall numberof edges connected to each of the check nodes remains the same. Inaddition or alternatively, the codebook modification module 1502 maymodify a codebook by swapping two or more columns of an associatedparity-check matrix with each other. One of the columns involved in theswapping may correspond to a bad variable node participating in aselected minimal cycle, and another of the columns involved in theswapping may correspond to a good variable node not participating in theselected minimal node.

To illustrate an example codebook modification based on numbers of badvariables participating minimal cycles, FIG. 17A shows a Tanner graph ofan existing codebook that may be included in the codebook database 508.The Tanner graph shown in FIG. 17A is the same as the Tanner graph shownin FIG. 16A. The Tanner graph includes a minimal cycle formed by thebolded edges shown in FIG. 17A, including an edge connecting the firstvariable node v(1) to the first check node c(1), an edge connecting thefirst check node c(1) to the third variable node v(3), an edgeconnecting the third variable node v(3) to the second check node c(2),and a final edge connecting the second check node c(2) to the firstvariable node v(1). A length of the minimal cycle is four, and a totalnumber of variable nodes participating in the minimal cycle is two.

Suppose in the example that the bad storage locations of the particularmemory area for which the existing codebook is being modified includesthe first storage location and the third storage location, as indicatedby the bolded boxes around those storage locations. As such, all of thevariable nodes participating in the identified minimal cycle areassociated with bad storage locations, yielding two participating badvariable nodes, a value of two for the difference between the length ofthe identified minimal cycle and the number of participating badvariable nodes, a value of 0.5 for the ratio of the number ofparticipating bad variable nodes to the length of the minimal cycle, avalue of zero for the difference between the total number ofparticipating variable nodes and the number of number of participatingbad variable nodes, and a value of one for the ratio of the number ofparticipating bad variable nodes to the total number of participatingvariable nodes. The codebook modification module 1502 may be configuredto calculate some or all of these values, and based on one or more ofthese values, identify this minimal cycle as a candidate minimal cycle.Also, as previously described, other values may be calculated based onthe number of bad variable nodes participating in the minimal cycle, thelength of the minimal cycle, and/or the total number of participatingvariable nodes, and the codebook modification module 1502 may use one ormore of these other values to identify the minimal cycle as a candidateminimal cycle.

In turn, the codebook modification module 1502 may be configured tomodify the codebook by removing or adjusting the connections to one ormore of the variable nodes participating in the identified minimal cycle(i.e., the first variable node v(1) and/or the third variable nodev(3)). FIG. 17B shows a Tanner graph of the modified codebook. As shownin FIG. 17B, the modification is performed by changing the check nodesto which edges connected to the first and third variable nodes areconnected. In particular, as denoted by the bolded edges, an edgeconnected to the first variable node v(1) and was initially connected tothe first check node c(1) is changed to being connected to the thirdcheck node c(3). In addition, an edge that connected to the thirdvariable node v(3) and was initially connected to the first check nodec(1) is changed to being connected to the fourth check node c(4).Additionally, FIG. 17B shows further connection modifications made tokeep the same the total number of connections to each of the four checknodes c(1) to c(4). In particular, and as indicated by the bolded edgesin FIG. 17B, an edge connected to the fourth variable node v(4) andinitially connected to the fourth check node c(4) is changed to beingconnected to the first check node c(1), and an edge connected to theninth variable node v(9) and initially connected to the third check nodec(3) is changed to being connected to the first check node c(1).

A result of the codebook modification shown in FIG. 17B is theoriginally identified short cycle is broken up or removed from thecodebook, and newly formed short cycles have improved minimal cyclemetrics. For example, a newly formed minimal cycle includes an edgeconnecting the first variable node v(1) to the second check node c(2),an edge connecting the second check node c(2) to the second variablenode v(2), an edge connecting the second variable node v(2) to the thirdcheck node c(3), and an edge connecting the third check node c(3) to thefirst variable node v(1). While the length and total number of variablenodes for the newly formed minimal cycle has stayed the same at four andtwo, respectively, the number of participating bad variable nodes isreduced from two to one (i.e., it includes only the first variable nodev(1) instead of both the first and third variable nodes v(1) and v(3)).Similarly, other newly minimal cycles may include both the first andthird variable nodes v(1) and v(3), but may have respective lengthslarger than 4 and/or include more than two participating variable nodes.

For simplicity, the example codebook modification illustrated in FIGS.17A and 17B shows modifying the codebook by identifying and removing asingle minimal cycle. In other example configurations, more than oneminimal cycle be identified and/or removed for a given permutation.Also, in the example codebook modification illustrated in FIGS. 17A and17B, the minimal cycle identified as a candidate minimal cycle was alsothe minimal selected to be the subject of the codebook modification. Inother example configurations, as mentioned, there may be more than oneminimal cycle identified as a candidate, but less than all of theminimal cycles are selected for modification. Various configurations forselecting minimal cycles for codebook modification based on number ofparticipating bad variable nodes may be possible.

In addition, the codebook modification module 1502 may be configured togenerate a single modification or permutation of an existing codebook ormultiple modifications. For example, with reference to FIGS. 16A-17B,the codebook modification module 1502 may determine several possibledifferent ways to modify the edges between the variable nodes and thecheck nodes in order to reduce the numbers of bad variables connected togiven check nodes and/or the numbers of bad variables participating inminimal cycles. In the event that the codebook modification module 1502generates multiple modifications or permutations, the controller 102,such as with the ECC engine 124, may be configured to identify a bestmodification. For example, the ECC engine 124 may be configured todetermine which modification yields the best decoding metrics, such aswas described with reference to FIG. 8, or may score each of themodifications or using the scoring scheme described with reference toFIGS. 11-14.

Additionally, the codebook modification module 1502 may be configured tomodify one or more existing codebooks to generate one or more modifiedcodebooks for one or more of the plurality of memory areas of the memorydies 104. Referring back to FIG. 15, the codebook modification module1502 may communicate with the memory area identification module 1504 toidentify a memory area for which to modify one or more codebooks. Insome example configurations, during a production phase, the codebookmodification module 1502 may communicate with the memory areaidentification module 1504 to cycle through the various memory areas ofthe memory dies 104 to determine whether and/or how to generate modifiedcodebooks based on the bad storage location information particular toeach of the memory areas. In addition or alternatively, during operationof the memory system 100, the codebook modification module 1502 maydetermine whether and/or how to modify one or more codebooks for aparticular memory area in response to degradation of decoding metricswhen decoding data from the memory area, such as based on an increasedamount of decoding time or number of decoding iterations to decode thedata.

In addition, as previously described, the codebook modification module1502, the memory area identification module 1504, and the bad storagedatabase 1506 may be components of the memory system 100, such ascomponents of the ECC engine 124 or another components of the controller102. In another example embodiment, the codebook modification module1502, the memory area identification module 1504, and the bad storagedatabase 1506 may be components of an external computing device orsystem, such as a testing device or system, that is external to thememory system 100. The external computing device may have access toand/or have stored therein a codebook library that contains existingcodebooks to, at least initially, be used to encode and decode data tobe stored in the various memory areas. Based on the bad storagelocations of the memory areas, the codebook modification module 1502 andthe memory area identification module 1504 may be configured to generatemodified codebooks as described with reference to FIGS. 15-17B. Theexternal computing device may then load the modified codebooks into thecodebook database 508 of the memory system 100 as the N-number ofcodebooks 506(1)-506(N) that the ECC engine 124 uses to encode anddecode data for the various memory areas of the memory dies 104.

In other example embodiments, some of the components shown in FIG. 15may be components of the memory system 100 and the other of thecomponents may be components of a controller of the external computingdevice. Which components are part of the memory system 100 and which arepart of the external computing device or system may vary. For theseembodiments, the components of the memory system 100 and the componentsof the external computing device or system may communicate with eachother in order to ultimately have the modified codebooks loaded into thecodebook database 508 of the memory system 100. Various ways ofintegrating the components shown in FIG. 15 into the memory system 100,an external computing device or system, or a combination thereof, may bepossible.

FIG. 18 shows a flow chart of an example method 1800 of a codebookmodification process that may generate one or more modified versions ofone or more existing codebooks for a plurality of memory areas. At block1802, the memory area identification module 1504 may identify a nextmemory area of the plurality of memory dies 104 for which to modify oneor more existing codebooks used to encode and decode data stored in thememory area. If the method 1800 is in its initial iteration, the nextmemory area may be an initial memory area that the memory areaidentification module 1504 is configured to identify. At block 1804, thecodebook modification module 1502 may determine the bad storagelocations of the memory area, such as by accessing the bad storagedatabase 1506.

At block 1806, the codebook modification module 1502 may generate amodified codebook for the memory area based on one or more existingcodebooks using the bad storage location information the codebookmodification module 1502 identified at block 2004. The codebookmodification module 1502 may do so using one or more of the codebookmodifications described with reference to FIGS. 15-17B, includingmodifying an codebook to reduce the number of bad variables connected toone or more check nodes or an existing codebook to reduce the number ofbad variables participating in one or more minimal cycles.

At block 1808, the codebook modification module 1502 may determinewhether there is another codebook modification to be made for thecurrent memory area. For example, as previously described, there may beseveral permutations of an existing codebook or sub-codebook for a givenset of bad storage locations. If so, then the method may proceed back toblock 1806, where the codebook modification module 1502 may generateanother modified codebook or another set of modified codebooks using thebad storage location information. Alternatively, if not, then the methodmay proceed to block 1810, where the codebook modification module mayidentify a best modified codebook or set of modified codebooks. Forexample, the codebook modification module 1502 may use the decodeevaluation module 810 and the codebook scoring chart 812 shown in FIG. 8to identify the modified codebook that yields the best decoding metrics.As another example, the codebook modification module 1502 may utilizethe codebook scoring module 1102 shown in FIG. 11 to score the modifiedcodebooks in order to choose the best one. In the event that thecodebook modification module 1502 generated only one modified codebookor a set of modified codebooks, then block 1810 may be skipped.

At block 1812, the memory area identification module 1504 may determinewhether there is another memory area for which to perform codebookmodification, if so, then the method may proceed back to block 1802,where a next memory area is identified for codebook modification. Ifnot, then the method may end.

In other example embodiments, the memory system 100 may be configured touse differently sized codebooks to generate differently sized codewordsin a page of data, or use differently sized sub-codebooks to generatedifferently sized sub-codewords in a codeword. The sizes for thecodebooks to generate differential sized codewords in a data page may bedetermined so that the ratio of the number of parity bits to the numberof bad bits for a given codeword is the same or as close as possible foreach of the codewords of a data page. Doing so may improve decoding byequalizing the error correction capability among the codewords in thedata page.

In further detail, and as previously explained with reference to FIG. 4,each codeword comprising an information bit sequence and parity bitsgenerated for the information bit sequence may be stored in a segment orunit of storage, and a plurality of units may make up a page of storage.Accordingly, the codewords stored or to be stored in a single storagepage may be or make up a page of data, otherwise referred to as a datapage.

The bad memory cells within a storage page of data may be unevenlydistributed. Accordingly, among a plurality of storage units within asingle storage page, the number of bad memory cells each storage unitmay be different. As a result, where the number of parity bits used toencode the codewords stored in a storage page is the same, codewordsstored in storage units having a higher number of bad memory cells maybe harder to decode compared to codewords stored in storage units havinga lower number of bad memory cells. This disparity in decodingperformance may be offset by adjusting the number of parity bits used toencode each of the codewords to be stored in a storage page based on thenumber of bad memory cells in each of the storage units.

FIG. 19 shows a block diagram of components of an example embodiment ofthe controller 102 that may be involved in determining sizes ofcodebooks used to generate codewords of the same data page. For someexample configurations, the components may be components of the ECCengine 124, although in other example configurations, some or all ofthese components may be considered components separate from the ECCengine 124. The components involved may include a codebook sizedetermination 1902, a memory area identification module 1904, a badstorage database 1906, which may identify bad storage locations for thevarious memory areas of the memory dies 104 as previously described, acodebook determination module 1908, and the codebook database 508, whichmay include an N-number of codebooks 1910 used to generate codewordsstored in an N-number of storage units 1912 of a given storage page 1914of a memory die 104. Also, in some example embodiments, the componentsmay include a codebook library 1916 storing an M-number of codebooks1918(1) to 1918(M).

In further detail, the N-number of storage units 1912 may include afirst storage unit 1912(1), a second storage unit 1912(2), and extendingto an Nth storage unit 1912(N). In general, there may be two or morestorage units 1912 per storage page 1914 (i.e., N is two or more). Thecodebook database 508 may include a first codebook 1910(1) that is usedto generate a first codeword stored in the first storage unit 1912(1), asecond codebook 1910(2) that is used to generate a second codewordstored in the second storage unit 1912(2), and extending to an Nthcodebook 1910(N) that is used to generate an Nth codeword stored in theNth storage unit 1912(N).

The codebook size determination module 1902 may be configured todetermine sizes (i.e., the number of columns and rows) for each of thecodebooks 1912. The codebook size determination module 1902 may make thesize determinations based on the bad storage locations and/or thenumbers of bad storage locations for the given storage page 1914 and/orfor each of the storage units 1912(1) to 1912(N). The codebook sizedetermination module 1902 may be configured to access the bad storagedatabase 1906 to determine the bad storage locations and/or the numbersof bad storage locations. If the bad storage locations are unevenlydistributed among the storage units 1912 of the given storage page 1914,then the codebook size determination module 1902 may determine that atleast two of the sizes of the codebooks 1910(1) to 1910(N) are to bedifferent from each other. In general, two codebooks may bedifferently-sized from each other by being configured to generatedifferent numbers of parity bits and/or by having associatedparity-check matrices with different numbers of columns, rows, or acombination thereof.

Despite having different sizes, the number of parity bits each of thecodebooks 1910(1) to 1910(N) is configured to generate may beproportionate to the number of bad memory cells in each of the storageunits 1912 of the given storage page 1914. In particular, the size ofthe codebooks 1910(1) to 1910(N) may be set so that the ratios of thenumber of parity bits to the number of bad memory cells for each of thestorage units 1912(1) to 1912(N) of the given storage page 1914 are thesame or as close as possible.

In some example configurations, the codebook size determination module1902 may consider the number of expected failed or incorrect bit values(FBC) of a read codeword from a storage unit 1912 as a result of the biterror rate (BER) associated with the channel over which the data iscommunicated between the controller 102 (and/or RAM 116) and the memorydie 104 that includes the given storage page 1914. The BER of thechannel may be known, and the number of expected incorrect bit valuesmay be the BER times the size of the storage unit 1914 (i.e., the numberof bits the storage unit 1914 is configured to store). The codebook sizedetermination module 1902 may then use the following two equations toidentify the parity bit values p_(i) for each ith storage unit 1912:

$\begin{matrix}{{\frac{p_{1}}{\left( {{FBC} + {BBL}_{1}} \right)} = {\frac{p_{2}}{\left( {{FBC} + {BBL}_{2}} \right)} = {\ldots = \frac{p_{N}}{\left( {{FBC} + {BBL}_{N}} \right)}}}},} & (14) \\{{{p_{1} + p_{2} + \ldots + p_{N}} = p_{TOTAL}},} & (15)\end{matrix}$where FBC is number of expected failed or incorrect bit values for astorage unit 1912, p₁ is the number of parity bits the first codebook1910(1) is to generate after codebook modification, BBL₁ is the numberof bad bit lines associated with the first storage unit 1912(1), p₂ isthe number of parity bits the second codebook 1910(2) is to generateafter codebook modification, BBL₂ is the number of bad bit linesassociated with the second storage unit 1912(2), p_(N) is the number ofparity bits the Nth codebook 1910(N) is to generate after codebookmodification, BBL_(N) is the number of bad bit lines associated with theNth storage unit 1912(N), and p_(TOTAL) is the total number of paritybits the data page (or the N-number of codewords) has. As previouslydescribed, the number of bad memory cells in a given storage unit 1804may be equal to the number of bad bit lines extending through the givenstorage unit 1804. The codebook modification module 1502 may identifythe numbers of parity bits p₁, p₂, . . . p_(N) using the constraintsimposed by equations 14 and 15—i.e., so that equations 14 and 15 areboth true.

Upon determining the sizes for each of the codebooks 1910(1) to 1910(N),the codebook size determination module 1902 may provide the sizes to thecodebook determination module 1908, which in turn may be configured todetermine each of the codebooks 1910(1) to 1910(N). In some exampleconfigurations, the codebook determination module 1908 may be configuredto generate, such as from scratch, each of the codebooks 1910(1) to1910(N) according to the size information received from the codebooksize determination module 1902. In other example configurations, thecodebook determination module 1908 may be configured to modify orpermute existing versions of the codebooks 1910 to generate new versionsof the codebooks 1910. For example, the N-number of codebooks 1910(1) to1910(N) may have an initial configuration in which they are the same aseach other, or at least have the same size as each other. For theinitial configurations, there may be a total number of parity bits thatthe initial codebook(s) 1910 is/are configured to generate for the givenstorage page 1914. After modifying or permuting the initial codebook(s)1910, at least two of the resulting new codebooks 1910(1) to 1910(N) maybe differently sized from each other, but the total number of paritybits that the new codebooks 1910(1) to 1910(N) are configured togenerate for the data page stored in the given storage page 1914 may bethe same as the initial configuration. As part of the modification, thecodebook determination module 1908 may be configured to add columns androws to increase sizes of existing codebooks or subtract columns androws to decrease sizes of existing codebooks in order to generate thenew codebooks 1910(1) to 1910(N). In addition to the adding and/orsubtracting of columns and rows, the codebook determination module 1908may be configured to change values within the parity-check matricesand/or swap columns and/or rows in order to generate modifiedparity-check matrices according to the size information received fromthe codebook size determination module 1902.

For other example configurations, the codebook determination module 1908may be configured to access the codebook library 1916 and select a setof the M-number of codebooks 1918 in the library 1916 to use for theN-number of codebooks 1910. For example, the M-number of codebooks1918(1) to 1918(M) stored in the codebook library 1916 may includedifferent sets of codebooks, with each set having differently sizedcodebooks from the other sets. Upon determining the numbers of paritybits p₁ to p_(N), such as by receiving the size information from thecodebook size determination module 1902, the codebook determinationmodule 1908 may select the set of codebooks that are configured togenerate or most closely generate the numbers of parity bits p₁ to p_(N)that the codebook size determination module 1902 determined. Uponselection, the selected set of codebooks may be loaded into the codebookdatabase 508 as the N-number of codebooks 1910(1) to 1910(N).

In another example configuration, the codebook size determination module1902 may identify the sizes of sub-codebooks on a sub-codeword level. Infurther detail, for some example encoding and decoding schemes, aninformation bit sequence β may be divided or separated into apredetermined n-number of portions, where n is two or more. An examplemay be a 4 kilobyte (kB) information bit sequence that is divided intofour 1 kB bit sequence portions. Sub-code parity bits may be generatedseparately for each of the information bit sequence portions.Additionally, joint parity bits may be generated collectively for thebit sequence portions.

FIG. 20A shows a block diagram of an example configuration of componentsof the parity bit generator module 502 (FIG. 5) that may be configuredto generate sub-code parity bits for information bit sequence portionsof a codeword. The components may include a sub-code parity generationmodule 2002 and a joint parity generation module 2004. Also, the RAM 116may be separated or organized into an information bit portion 2006designated for storage of information bits of a codeword, a sub-codeparity bit portion 2008 designated for storage of sub-code parity bitsof the codeword, and a joint parity bit portion 2010 designated forstorage of joint parity bits of the codeword.

The unencoded information bit sequence β may be initially stored in theinformation bit portion 2006. The sub-code parity generation module 2002may encode an n-number of portions of the information bit sequence βusing one or more sub-codebooks in order to generate an n-number ofsub-code parity bit sequences δ, each for one of the portions of theinformation bit sequence β. Each parity bit sequence δ may be furtherdivided into a first sub-code parity bit portion δ′ and a first jointparity bit portion δ″. The first sub-code parity bit portion δ′ may betransferred to the sub-code parity bit portion 2008 of the RAM 116. Thecombination of the first sub-code parity bit portion δ′ and theassociated portion of the information bit sequence β for which the firstsub-code parity bit portion δ′ is generated may form a sub-codeword.Additionally, the first joint parity bit portion δ″ may be sent to thejoint parity generation module 2004 for further processing as describedin further detail below.

To illustrate, the sub-code parity generation module 2002 may encode afirst portion of the information bit sequence β using a sub-codebook inorder to generate a first parity bit sequence δ₁. The first parity bitsequence δ₁ may be divided into a first sub-code parity bit portion δ₁′and a first joint parity bit portion δ₁″. The first sub-code parity bitportion δ₁′ maybe transferred to the sub-code parity bits portion 2006of the RAM 116, and the first portion of the information bit sequence βcombined with the first sub-code parity bit portion δ₁′ may form a firstsub-codeword corresponding to the information bit sequence β.Additionally, the first joint parity bit portion δ₂″ may be sent to thejoint parity generation module 2004. Further, the sub-code paritygeneration module 2002 may also encode a second portion of theinformation bit sequence β using a sub-codebook in order to generate asecond parity bit sequence δ₂. The second parity bit sequence δ₂ may bedivided into a second sub-code parity bit portion δ₂′ and a second jointparity bit portion δ₂″. The second sub-code parity bit portion δ₂′ maybe transferred to the sub-code parity bits portion 2006 of the RAM 116.The second portion of the information bit sequence β combined with thesecond sub-code parity bit portion δ₂′ may form a second sub-codewordcorresponding to the information bit sequence β. The second joint paritybit portion δ₂″ may be sent to the joint parity generation module 2004.The encoding process may continue in this manner until all of then-number of portions of the information bit sequence β are encoded bythe sub-code generation module 2002 and sub-code parity bit portions δ′are generated for each of the information bit portions and stored in thesub-code parity bit portion 2008 of the RAM 116.

The joint parity generation module 2004 may be configured to generatethe joint parity bits for the codeword by performing a bitwise XORoperation on the joint parity bit portions δ″. The result of the XORoperation(s), referred to as a combined joint parity bit portion δ′″,may be the joint parity for the codeword and stored in the joint paritybits portion 2010 of the RAM 116. A complete codeword stored in asegment may be a combination of the sub-codewords and the combined jointparity bit portion δ′″.

For decoding a codeword generated with the encoding process performedwith the components of FIG. 20A, the ECC engine 124 (FIG. 2A) may decodethe sub-codewords individually without using the combined joint paritybits δ′″. However, if during the decoding, the ECC engine 124 determinesthat one or more of the bit error rates associated with thesub-codewords is too high, then the ECC engine 124 may decode thesub-codewords by combining the sub-codewords and also using the combinedjoint parity bits δ′″. Decoding using the sub-code parity δ′ and withoutthe combined joint parity δ′″ may be referred to as the normal ordefault mode, and decoding using the sub-code parity δ′ and the combinedjoint parity bits δ′″ may be referred to as a heroics mode.

Referring to FIG. 20B, the sub-code parity generation module 2002 may beconfigured to generate the n-number of sub-code parity bit sequencesusing an n-number of sub-codebooks 2002 loaded into the codebookdatabase 508, including a first sub-codebook 2002(1) to generate thefirst sub-code parity bits δ₁ 2004(1) for a first portion of theinformation bit sequence β, a second sub-codebook 2002(2) to generatethe second sub-code parity bits δ₂ 2004(2), and extending to an nthsub-codebook 2002(n) to generate the nth sub-code parity bits δ_(n)2004(n).

Referring to FIG. 20C, sub-parity-check matrices H_(sc1) to H_(scn)associated with the sub-codebooks 2002(1) to 2002(n) may be and/orcorrespond to submatrix portions of a larger parity-check matrix Hassociated with the entire codeword. FIG. 20C shows a schematic diagramof an example configuration of a larger parity-check matrix H. Then-number of number of parity check matrices H_(sc1) to H_(scn) maycorrespond and/or be equal to the n-number of portions of theinformation bit sequence β and/or the number of sub-codewords that aregenerated. The example parity-check matrix H shown in FIG. 20C includesfour sub-matrices H_(sc1), H_(sc2), H_(sc2), H_(sc4) (i.e., n=4),although as mentioned, numbers other than four may be possible. Eachsub-matrix H_(sc) may include one or more columns 2050 corresponding tothe sub-code parity and one or more columns 2052 corresponding to parityused to generate the joint parity bits. Also the larger parity-checkmatrix H may include a joint sub-matrix H_(joint) corresponding to thejoint parity bits. The joint sub-matrix H_(joint) may include columns inalignment with and/or part of the same column as the columns 2052 of thesub-matrices H_(sc). These columns 2054 may include elements having bitvalues of ones or a combination of zeros and ones. The elements of thejoint sub-matrix H_(joint) outside of the columns 2054 may all have bitvalues of zeros. In some example configurations, the joint sub-matrixH_(joint) may be input and/or used by the joint parity generation module2004 for generation of the joint parity bits.

Referring to FIG. 21, the codebook size modification module 1902 may beconfigured to identify sizes for the sub-codebooks 2002(1) to 2002(n) ina way that is similar to the way it identified the sizes of thecodebooks 1910(1) to 1910(N), as described with reference to FIG. 19.Upon accessing the bad storage database 1906, the codebook sizedetermination module 1902 may determine that the bad storage locationsare unevenly distributed among the storage sub-units 2008(1) to 2008(n)of the given storage unit 2006. In a particular example configuration,the codebook size determination module 1902 may be configured to set thesub-code parity bits each sub-codebook 2002 is configured to generate sothat the ratios of the number of sub-code parity bits to the number ofbad memory cells for each of the storage sub-units 2008(1) to 2084(n) ofthe given storage unit 2006 are the same or as close as possible.Additionally, the codebook size identification module 1902 may beconfigured to use equations (14) and (15) above to determine how to setthe sizes of the sub-codebooks 2002(1) to 2002(n), except that in thiscase, p_(i) represents the number of sub-code parity bits generated foran ith sub-codeword, p_(TOTAL) represents the total number of sub-codeparity bits generated for the codeword, FBC represents the number ofexpected number of failed or incorrect bits values for a given sub-unit2008, and BBL represents the number of bad bit lines in the ith storagesub-unit 2008(i).

In addition, upon determining the sizes for each of the sub-codebooks2002(1) to 2002(N), the codebook size determination module 1902 mayprovide the sizes to the codebook determination module 1908, which inturn may be configured to determine each of the sub-codebooks 2002(1) to2002(N). In some example configurations, the codebook determinationmodule 1908 may be configured to generate, such as from scratch, each ofthe sub-codebooks 2002(1) to 2002(n) according to the size informationreceived from the codebook size determination module 1902. In otherexample configurations, the codebook determination module 1908 may beconfigured to modify or permute initial or existing versions of thesub-codebooks 2002 to generate new versions of the sub-codebooks 2002,such as by adding or subtracting rows and columns to associated sub-codematrices H_(sc) according to the size information. For these exampleconfigurations, the total number of sub-code parity bits that aregenerated by the sub-codebooks 2002(1) to 2002(n) after modification mayremain the same compared to the initial versions. In other exampleconfigurations, the codebook determination module 1908 may be configuredto access a codebook library 2102 and select a set sub-codebooks from anM-number of sub-codebooks 2104(1) to 2104(M) in the library 1916 thatcorresponds to the size information received from the codebook sizedetermination module 1902. Upon making the selection, the codebookdetermination module 1908 may load the selected set into the codebookdatabase 508 for use as the N-number of sub-codebooks 2002(1) to2002(n).

In other example configuration of codebook modification, the codebooksize determination module 1902 may be configured to identify sizes ofcodebooks and/or sub-codebooks based on mutual information (MI)associated with the codewords. In general, the memory system 100 mayinclude a channel over which a codeword is transmitted from the RAM 116to the memory dies 104 for programming into a given storage unit, andthen over which the programmed codeword is transmitted from the givenstorage unit of the memory dies 104 back into the RAM 116 as part of aread operation. The version of the codeword prior to being communicatedover the channel and programmed into the memory dies 104 unit may bereferred to as the input codeword, and the version of the codeword afterit is read back out of the memory dies 104 may be referred to as theoutput codeword. The channel is generally noisy, meaning that the outputcodeword will have errors, i.e., the logic levels of the bit sequence ofthe output codeword will not match the logic levels of the bit sequenceof the input codeword. One characteristic of the channel may be itschannel capacity, which may be a tight upper bound on the bit rate atwhich the codeword can be reliably transmitted over the channel. Mutualinformation of the channel may determine the channel's channel capacity.In particular, the channel's channel capacity may be maximum mutualinformation with respect to an input distribution of the input codeword.In actual implementation, the memory system 100 may communicate thecodeword over the channel at a bit rate that is lower than the mutualinformation. A rate gap (or simply gap), may be a known value thatdefines an upper bound for the bit rate. That is, the memory system 100may be configured to communicate the codeword over the channel at a bitrate that is lower than the mutual information minus the gap, asrepresented by the following inequality:R<MI−G,  (16)where R represents the bit rate at which the codeword is transmittedover the channel, MI represents the mutual information of the channel,and G represents the gap.

For a given codeword, the channel that communicated the codeword and thestorage unit storing the codeword may be referred to as being associatedwith and/or corresponding to each other. The mutual information of agiven channel and/or the associated storage unit may be based on anassociated error count, which may be the sum of the number of expectedfailed or incorrect bit values (FBC) of the codeword transmitted on thegiven channel and the number of bad bit lines (BBL) of the associatedstorage unit storing the codeword (the number of bad bit lines may alsobe referred to as the number of erasures). In particular, the mutualinformation of a given channel may be calculated using and/or based onthe following equations:MI(X,Y)=H(X,Y)−H(X)−H(Y),  (17)where X is the set of bit values of the bits of a codeword as the bitvalues were programmed into a storage unit of the memory dies 104, Y isthe set of bits values of the bits of the codeword as the bit valueswere identified (e.g., by the ECC engine 124) upon being read from thestorage unit over the given channel, and H is the entropy defined as:H(X,Y)=−Σ_(x∈X,y∈Y) P(x,y)log₂ P(x,y),  (18)H(X)=−Σ_(x∈X) P(x)log₂ P(x)  (19)H(Y)=−Σ_(y∈Y) P(y)log₂ P(y),  (20)where x denotes a bit value of the set of initially programmed bitsvalues X and y denotes a corresponding bit value of the set of read bitvalues Y. For the given channel, the conditional probability ofreceiving a bit value y given a corresponding bit value x, denoted asP(y|x), may be calculated based on a model. One example model may be abinary symmetric model. Another model example may add noise, such as aGaussian distributed noise, to each voltage level associated with eachbit, which may yield various conditional probability P(y|x) values foreach of the bit values in the sets X and Y. Other models may bepossible. The number of expected failed or incorrect bit values (FBC)and the number of bad bits in the read codeword (i.e, the number oferasures or bad bit lines extending through the storage unit) may beinputs to and/or define the model used to define the conditionalprobability P(y|x) values. The programmed bit value distribution P(x)may be known. Accordingly, upon determining the conditional probabilityP(y|x) values, the joint distribution P(x,y) and the marginaldistribution P(y) may be determined according to the followingequations:P(x,y)=P(x)P(y|x),  (21)P(y)=Σ_(x∈X) P(x,y).  (22)Upon determining the programmed bit value distribution P(x), the jointdistribution P(x,y), and the marginal distribution P(y), the mutualinformation may be calculated using equations (17)-(20).

The bit rate at which a codeword is transmitted over the channel mayalso be a function of the number of parity bits of the codeword. Inparticular, the bit rate may be determined by the following equation:

$\begin{matrix}{{R = \frac{I}{p + I}},} & (23)\end{matrix}$where R represents the bit rate of the codeword, p represents the numberof parity bits of the codeword, and I represents the number ofinformation bits of the codeword. Combining equations (16) and (23), anupper bound for the number of parity bits p of the codeword can bedetermined as a function of the number of information bits I, the mutualinformation, and the gap, as indicated by the following inequality:

$\begin{matrix}{p > {\frac{I\left( {{MI} - G - 1} \right)}{G - {MI}}.}} & (24)\end{matrix}$

Referring back to FIG. 19, the codebook sized determination module 1902may be configured to identify the sizes for the codebooks 1910(1) to1910(N) based on associated mutual information. A given ith codebook1910(i) may be associated with mutual information of a given channel ifthe channel is used to communicate a codeword that was generated usingthe ith codebook 1910(i). For example, the first codebook 1910(1) isused to generate parity bits for a codeword stored in the first storageunit 1910(1) of the storage page 1802, and so the mutual information ofthe channel used to communicate a codeword stored in the first storageunit 1910(1) may be considered to be associated with the first codebook1806(1).

To determine the sizes for the codebooks 1910(1) to 1910(N), thecodebook size determination module 1902 may determine the mutualinformation associated with each of the codebooks 1910(1) to 1910(N). Todo so, the codebook modification module 102 may access the bad storagedatabase 1906 to identify the bad storage locations for the givenstorage page 1914 and/or for each of the storage units 1912(1) to1912(N). If the bad storage locations are unevenly distributed over thestorage units 1912(1) to 1912(N), then the codebook size determinationmodule 1902 may determine that at least two of the codebooks 1910(1) to1910(N) will be differently sized from each other based on theassociated mutual information. In particular, the codebook modificationmodule 1502 may be configured to determine error counts for each of thestorage units 1912(1) to 1912(N). As previously described, for a givenith storage unit 1912(i), the associated error count may be the sum ofthe expected failed or incorrect bit values (FBC) of a codeword readfrom the given storage unit 1912(i) and the number of bad bit lines(BBL_(i)) associated with the given storage unit 1912(i). The codebooksize determination module 1902 may be configured to determine the numberof associated bad bit lines based on the bad storage locationinformation obtained from the bad storage database 1906. The codebooksize determination module 1902 may then be configured to determine amutual information value associated with each of the codebooks 1910(1)to 1910(N) based on the associated error counts, such as by using one ormore of equations (17)-(20) above. Then, using equation (22), thecodebook size determination module 1902 may be configured to determineamounts of parity bits to be generated by each of the codebooks 1910(1)to 1910(N), with the additional constraint that the total number ofparity bits generated by the codebooks 1910(1) to 1910(N) may not exceedthe initial number of parity bits p_(TOTAL) of a data page stored in thestorage page 1914, as represented by the following inequality:p ₁ +p ₂ + . . . +p _(N) ≤p _(TOTAL)  (25)Upon determining the sizes for each of the codebooks 1910(1) to 1910(N),the codebook size determination module 1902 may send the sizeinformation to the codebook determination module 1908. In response, thecodebook determination module 1908 may determine the codebooks 1910(1)to 1910(N) in the same way as previously described.

In another example configuration, the codebook size determination module1902 may be configured to identify sizes for sub-codebooks based onmutual information on a sub-code level. Referring back to FIG. 20B, fora given storage unit 2006, if the bad storage locations are unevenlydistributed across the storage sub-units 2008(1) to 2008(n), then thecodebook size determination module 1502 may identify the sizes of two ormore sub-matrices H_(sc) to be different from each other based on mutualinformation associated with each of the sub-codebooks 2002(1) to2002(n). The codebook size determination module 1902 may be configuredto determine the numbers of sub-code parity bits for each of thesub-codewords using equations (16)-(25), except that p may represent thenumber of sub-code parity bits of a sub-codeword, I may represent thenumber of information bits of a sub-codeword, and p_(TOTAL) mayrepresent the number of parity bits of a codeword.

Additionally, the codebook size determination module 1902 may beconfigured to identify sizes for an N-number of codebooks 1910(1) to1910(N) and/or an n-number of sub-codebooks 2002(1) to 2002(n) for oneor more of the plurality of memory areas of the memory dies 104.Referring to either FIG. 19 or 21, the codebook size determinationmodule 1902 may communicate with the memory area identification module1904 to identify a memory area for which to determine sizes of codebooksand/or sub-codebooks. In some example configurations, during aproduction phase, the codebook size determination module 1902 maycommunicate with the memory area identification module 1904 to cyclethrough the various memory areas of the memory dies 104 to determinesizes for codebooks and/or sub-codebooks for the respective memory areasbased on the bad storage location information particular to each of thememory areas. In addition or alternatively, during operation of thememory system 100, the codebook size determination module 1902 maydetermine whether new sizes for codebooks and/or sub-codebooks for aparticular memory area in response to degradation of decoding metricswhen decoding data from the memory area, such as based on an increasedamount of decoding time or number of decoding iterations to decode thedata.

In addition, as previously described, the codebook size determinationmodule 1902, the memory area identification module 1904, the bad storagedatabase 1906, and the codebook determination module 1908 may becomponents of the memory system 100, such as components of the ECCengine 124 or another components of the controller 102. In other exampleembodiments, the codebook size determination module 1902, the memoryarea identification module 1904, the bad storage database 1906, and thecodebook determination module 1908 may be components of an externalcomputing device or system, such as a testing device or system, that isexternal to the memory system 100. In some of these embodiments, theexternal computing device may have access to and/or have stored thereinthe codebook library 1916. Based on the bad storage locations of thememory areas, the codebook size determination module 1902 may beconfigured to identify sizes for the codebooks and/or sub-codebooks ofthe various memory areas, and the codebook determination module 1908 maybe configured to determine the codebooks and/or sub-codebooks based onthe size information received from the codebook size determinationmodule 1092. The external computing device may then load the codebooksand/or sub-codebooks into the codebook database 508. Thereafter, such asduring normal operation of the memory system 100, the ECC engine 124 mayuse the loaded codebooks and/or sub-codebooks with the varying sizes toencode and decode data for the various memory areas of the memory dies104.

In other example embodiments, some of the components shown in FIGS. 19and 21 may be components of the memory system 100 and the other of thecomponents may be components of a controller of the external computingdevice or system. Which components are part of the memory system 100 andwhich are part of the external computing device or system may vary. Forthese embodiments, the components of the memory system 100 and thecomponents of the external computing device or system may communicatewith each other in order to ultimately have the determined codebooksloaded into the codebook database 508 of the memory system 100. Variousways of integrating the components shown in FIGS. 19 and 21 into thememory system 100, an external computing device or system, or acombination thereof, may be possible.

FIG. 22 shows a flow chart of an example method 2200 of a codebookdetermination process that may determine codebooks based on sizedeterminations for the codebooks for a plurality of memory areas. Insome example methods, a particular memory area may be a plane or aparticular storage page, and codebooks and associated sizes of codebooksare determined for storage pages in that plane or particular storagepage.

At block 2202, the memory area identification module 1904 may identify anext memory area of the plurality of memory dies 104 for which todetermine codebooks used to encode and decode data stored in the memoryarea. If the method 2200 is in its initial iteration, the next memoryarea may be an initial memory area that the memory area identificationmodule 1904 is configured to identify. At block 2204, the codebook sizedetermination module 1902 may determine the bad storage locations and/orthe numbers of bad storage locations of the memory area, such as byaccessing the bad storage database 1906.

At block 2206, the codebook size determination module 1902 may determinesizes for a set of codebooks used and/or numbers of parity bitsgenerated by the set of codebooks to encode and decode data stored inthe memory area identified at block 2202. If the bad storage locationsare unevenly distributed across the memory area, then at least two ofthe codebooks may be configured to generate different numbers of paritybits and/or associated parity-check matrices may be differently sized.The codebook size determination module 1902 may determine the sizesbased on ratios of parity bits to bad bits in codewords, such that theratio of the number of parity bits to the number of bad bits for a givencodeword stored in a storage unit of the memory area is the same or asclose as possible for a plurality of codewords stored in the samestorage page of the memory area, as previously described. In addition oralternatively, the codebook size determination module 1902 may determinethe sizes based on mutual information associated with each of thecodewords stored in the same storage page of the memory area. Thecodebook size determination module 1902 may then use the associatedmutual information to determine sizes and/or a number of parity bitseach codebook is to generate, such as by using equations (16)-(25), aspreviously described.

At block 2208, the codebook size determination module 1902 may providethe size information determined at block 2206 to the codebookdetermination module 1908. In response, at block 2210, the codebookdetermination module 1908 may determine codebooks for the storage unitsof the memory area. In some example methods, the codebook determinationmodule 1908 may determine the codebooks by generating the codebooksaccording to the size information. In other example methods, thecodebook determination module 1908 may determine the codebooks byselecting the codebooks from the codebook library 1916 using the sizeinformation receive from the codebook size determination module 1902.

At block 2212, the codebook determination module 1908 may load thecodebooks into the codebook database 508. In some example methods, thecodebook determination module 1908 may not load the determined codebooksinto the codebook database 508 until after the codebook determinationmodule 1908 has determined codebooks for all of the memory areas. Atblock 2214, the memory area identification module 1904 may determinewhether there is another memory area for which to determine codebooks.If so, then the method may proceed back to block 2202, where a nextmemory area is identified. If not, then the method may end.

FIG. 23 shows a flow chart of an example method 2300 of a sub-codebookdetermination process that may determine sub-codebooks based on sizedeterminations for the sub-codebooks for a plurality of memory areas. Insome example methods, a particular memory area may be a sub-plane or aparticular storage unit, and sub-codebooks and associated sizes ofsub-codebooks are determined for storage units in that sub-plane orparticular storage unit.

At block 2302, the memory area identification module 1904 may identify anext memory area of the plurality of memory dies 104 for which todetermine sub-codebooks used to encode and decode data stored in thememory area. If the method 2300 is in its initial iteration, the nextmemory area may be an initial memory area that the memory areaidentification module 1904 is configured to identify. At block 2304, thecodebook size determination module 1902 may determine the bad storagelocations and/or the numbers of bad storage locations of the memoryarea, such as by accessing the bad storage database 1906.

At block 2306, the codebook size determination module 1902 may determinesizes for a set of sub-codebooks used and/or numbers of parity bitsgenerated by the set of sub-codebooks to encode and decode data storedin the memory area identified at block 2202. If the bad storagelocations are unevenly distributed across the memory area, then at leasttwo of the sub-codebooks may be configured to generate different numbersof parity bits and/or associated subcode parity-check matrices may bedifferently sized. The codebook size determination module 1902 maydetermine the sizes based on ratios of parity bits to bad bits insub-codewords, such that the ratio of the number of parity bits to thenumber of bad bits for a given sub-codeword stored in a storage sub-unitof the memory area is the same or as close as possible for a pluralityof sub-codewords stored in the same storage unit of the memory area, aspreviously described. In addition or alternatively, the codebook sizedetermination module 1902 may determine the sizes based on mutualinformation associated with each of the sub-codewords stored in the samestorage unit of the memory area. The codebook size determination module1902 may then use the associated mutual information to determine sizesand/or a number of parity bits each sub-codebook is to generate, such asby using equations (16)-(25), as previously described.

At block 2308, the codebook size determination module 1902 may providethe size information determined at block 2306 to the codebookdetermination module 1908. In response, at block 2310, the codebookdetermination module 1908 may determine sub-codebooks for the storagesub-units of the memory area. In some example methods, the codebookdetermination module 1908 may determine the sub-codebooks by generatingthe sub-codebooks according to the size information. In other examplemethods, the codebook determination module 1908 may determine thesub-codebooks by selecting the sub-codebooks from the codebook library1916 using the size information receive from the codebook sizedetermination module 1902.

At block 2312, the codebook determination module 1908 may load thesub-codebooks into the codebook database 508. In some example methods,the codebook determination module 1908 may not load the determinedsub-codebooks into the codebook database 508 until after the codebookdetermination module 1908 has determined sub-codebooks for all of thememory areas. At block 2314, the memory area identification module 1904may determine whether there is another memory area for which todetermine sub-codebooks. If so, then the method may proceed back toblock 2302, where a next memory area is identified. If not, then themethod may end.

In other example embodiments, the memory system 100 may utilize acombination of codebook modification and size modification to determinecodebooks for a given memory area. For example, the codebookdetermination module 1908 may determine a set of codebooks to encode anddecode codewords stored in storage page, or a set of sub-codebooks toencode and decode sub-codewords stored in a storage unit, based on sizeinformation received from the codebook size determination module 1902.Thereafter, the codebook modification module 1502 may perform a codebookmodification process to modify one or more of the codebooks orsub-codebooks in the set, such as based on the numbers of bad variablesconnected to check nodes and/or the numbers of variables participatingin minimal cycles, as described with reference to FIGS. 15-17B. In otherexample embodiments, the codebook size determination module 1902 andcodebook determination module 1904 may be configured to analyze the badstorage locations across a given storage page to determine a set ofcodebooks for the given storage page, and also bad storage locationsacross the individual data units of the given storage page to determineto sub-codebooks or sub-matrices within each of the codebooks in thesets.

In other example embodiments, instead of evaluating a plurality ofcodebooks from a library based on decoding metrics (as described withreference to FIGS. 8-10), using a scoring algorithm (as described withreference to FIGS. 11-14), modifying one or more codebooks and/orsub-codebooks (as described with reference to FIGS. 15-18), ordetermining sets of codebooks and/or sub-codebooks based on codebooksize information (as described with reference to FIGS. 19-23), thememory system 100 may leverage information about the bad storagelocations of a memory area to improve decoding performance by using thebad storage location information to modify a bit sequence of a codewordafter encoding but before the codeword is stored in the memory area.

FIG. 24 shows a block diagram of components of an example embodiment ofthe controller 102 that may be involved in codeword modification basedon bad storage location information of a memory area. For some exampleconfigurations, the components other than the RAM 116 may be componentsof the ECC engine 124, although in other example configurations, some orall of these components may be considered components separate from theECC engine 124. In addition to the RAM 116, the components involved inthe codeword modification process may include a parity bit generatormodule 2402, a codeword modification module 2404, a bad storage database2406, and a decoder module 2410.

As previously described with reference to FIG. 5, when a host wants datastored in the memory dies 104, the data may be first stored in the RAM116 as unencoded information bits. The parity bit generator module 2402may generate parity bits for unencoded information bits, and theinformation bits combined with the parity bits may form an originalcodeword, which may be stored in the RAM 116. Upon the codeword beingformed, the codeword modification module 2404 may be configured toaccess the RAM 116 and change the bit order or bit sequence of theoriginal codeword in order to generate a modified codeword. Themodification may be based on the bad storage location information of thememory area in which the codeword is to be stored. In order to modifythe original codeword, the codeword modification module 2404 may beconfigured to identify the bad storage location information, such as byaccessing the bad storage database 2406. Further details how theencoder-side codeword modification module 2404 may modify the originalcodeword based on the bad storage location information is described infurther detail below.

After the codeword modification module 2404 generates the modifiedcodeword, the modified codeword may be sent to the memory dies 104 viathe sequencer module 126 and the memory interface 130, where themodified codeword is programmed into the memory area. When the modifiedcodeword is read from the memory area, such as in response to a hostread request, the modified codeword may be transferred into the RAM 116.The codeword modification module 2404 may then be configured to unmodifyor reverse modify the modified codeword so that the codeword is in itsoriginal form prior to modification. Thereafter, the decoder module 2408may decode the original codeword, and the decoded information bits maybe stored in the RAM 116 for transfer to the host to complete the readrequest.

In general, the codeword modification module 2404 may be configured tomodify a codeword by changing the order of the bit sequence, which inturn, affects which bits of the codeword are stored in which memorycells of the storage unit that is to store the codeword. The codewordmodification module 2404 may use the bad storage location information todetermine which bits to change.

In one example configuration of codeword modification, the codewordmodification module 2404 may modify the bit sequence of the codewordbased on numbers of bad variables connected to check nodes. Aspreviously described with reference to FIGS. 15, 16A and 16B, thecodebook modification module 1502 may identify which variable nodes arebad variable nodes and modify the codebook based on identifyingcandidate check nodes that are connected to a relatively high number ofbad variable nodes. In the example described with reference to FIGS. 16Aand 16B, the codebook modification module 1502 identified the secondcheck node c(2) as a candidate check node since it was connected tothree bad variables nodes, v(2), v(7), and v(12). As described, one waythe codebook modification module 1502 could modify the codebook is bychanging one edge connected to the second variable v(2) from beingconnected to the second check node c(2) to being connected to the firstcheck node c(1), and also changing another edge connected to the fifthvariable v(5) from being connected to the first check node c(1) to beingconnected to the second check node c(2), which is shown in FIG. 16B.

The codeword modification module 2404 may be configured to identifycandidate check nodes the same way that the codeword modification module1502 identified candidate check nodes. However, instead of modifying thecodebook by changing the edges, the codeword may be generated using theexisting codebook, and after the codeword is generated, the codewordmodification module 2404 may swap the second bit associated with thesecond variable node v(2) with the fifth bit associated with the fifthvariable node v(5). Swapping the second and fifth bits effectively makesthe fifth variable node v(5) a bad variable node and the second variablenode v(2) a good variable node, and in turn effectively reduces thenumber of bad variable nodes connected to the second variable node c(2).Thus, the problem of decoding performance being degraded by having checknodes connected to too many bad variable nodes may be alleviated byperforming bit swapping instead of codebook modification.

In another example configuration of codeword modification, the codewordmodification module 2404 may modify the bit sequence of the codewordbased on numbers of bad variables participating in minimal cycles. Aspreviously described with reference to FIGS. 15, 17A and 17B, thecodebook modification module 1502 may identify which variable nodes arebad variable nodes and modify the codebook based on identifyingcandidate minimal cycles that have a relatively large number of badvariable nodes participating in them. In the example described withreference to FIGS. 17A and 17B, the codebook modification module 1502identified a minimal cycle that includes bad variable nodes v(1) andv(3). The codebook modification module 1502 modified the codebook bybreaking up the candidate minimal cycle. In particular, the codebookmodification module 1502 changed an edge connected to the first variablenode v(1) from being connected to the first check node c(1) to beingconnected to the third check node c(3), an edge connected to the thirdvariable node v(3) from being connected to the first check node c(1) tobeing connected to the fourth check node c(4), an edge connected to thefourth variable node v(4) from being connected to the fourth check nodec(4) to being connected to the first check node c(1), and an edgeconnected to the ninth variable node v(9) from being connected to thethird check node c(3) to being connected to the first check node c(1),as was previously described with reference to FIG. 17B.

The codeword modification module 2404 may be configured to identifycandidate minimal cycles and bad variable nodes participating in thecandidate minimal cycles the same way that the codeword modificationmodule 1502 identified them. However, instead of modifying the codebookby changing the edges, the codeword may be generated using the existingcodebook, and after the codeword is generated, the codeword modificationmodule 2404 may swap the first and third bits associated with the firstand third variable nodes v(1), v(3) with the fourth and ninth bitsassociated with the fourth and ninth variable nodes v(4), v(9). Swappingthe first and third bits with the fourth and ninth bits effectivelymakes the fourth and ninth variable nodes v(4), v(9) bad variable nodesand the first and third variable nodes v(1), v(3) good variable nodes.The result of the swapping may effectively reduce the proportion of badvariable nodes participating in minimal cycles. Thus, the problem ofdecoding performance being degraded by having too many bad variablenodes participating in minimal cycles may be alleviated by performingbit swapping instead of codebook modification.

In another example configuration of codeword modification, the codewordmodification module 2404 may modify the bit sequence of the codewordbased on the distribution of bad storage locations over a storage unit.As previously described with reference to FIGS. 20A-20C, sub-codewordsmay be generated using one or more sub-codebooks. However, instead ofdetermining sizes for sub-codebooks and determining the sub-codebooksbased on the sizes as described with reference to FIGS. 20A-20C and 21,the codeword modification module 2404 may be configured to swap bitsacross sub-codewords such that the same number of bad bits, or as closeto the same number of bad bits as possible, will be included in eachread sub-codeword that is decoded by the ECC engine 124.

To illustrate, suppose a codeword includes four sub-codewords, includinga first sub-codeword that is to be stored in a first storage sub-unit ofa storage unit, a second sub-codeword that is to be stored in a secondstorage sub-unit of the storage unit, a third sub-codeword that is to bestored in a third storage sub-unit of the storage unit, and a fourthsub-codeword that is to be stored in a fourth storage sub-unit of thestorage unit. In addition, suppose that each sub-codeword has the samesize. Further, suppose that the bad storage database 2406 indicates thatthe first storage sub-unit includes one bad memory cell, the secondstorage sub-unit includes five bad memory cells, the third storagesub-unit includes three bad memory cells, and the fourth storagesub-unit includes three bad memory cells. After generating the foursub-codewords, the codeword modification module 2404 may be configuredmodify the bit order of the codeword such that two good bits (i.e., bitsto be stored in good memory cells) from the first sub-codeword areswapped with two bad bits (i.e., bits to be stored in bad memory cells)from the second sub-codeword, which effectively turns the two good bitsinto bad bits, and the two bad bits into good bits. As a result, eachsub-codeword of the modified codeword includes three bad bits.Subsequently, when the modified codeword is read from the memory dies104, the pairs of bits are re-swapped so that the codeword is in itsoriginal bit sequence. But when the decoder module 2408 decodes thesub-codeword, there will still be three bad bits in each sub-codewordthat the decoder module 2408 decodes. Swapping bits among sub-codewordsprior to programming the codeword such that the number of bad bits ineach read sub-codeword are the same may improve decoding performance(e.g., correction capability) of the decoder module 2408, compared tosituations where some sub-codewords have larger amounts of bad bits thanothers.

Although the codeword modification module 2404 is described withreference to FIG. 24 as being a component of the controller 102, inother example configurations, the codeword modification module 2404 maybe located on the memory dies. For these other example configurations,the codeword in its original form may be sent to the memory dies 104 viathe sequencer module 126 and the memory interface 130. Once the codewordis sent to the dies, the codeword modification module 2204 may modifythe codeword, and program the modified codeword into the memory area.Additionally, when a read request is issued to read the codeword, themodified codeword may be re-configured into its original form by thecodeword modification module 2404 before being sent off-chip to thecontroller 102. Other configurations may be possible. For example,codeword modification may be performed on the memory dies 104, but thenthe reconfiguring of the modified codeword into its original form may beperformed in the controller 102, or vice versa. Various configurationsmay be possible.

FIG. 25 is a flow chart of an example method 2500 of performing codewordmodification based on bad storage location information. At block 2502,the parity bit generator module 2402 may generate parity bits for aninformation bit sequence using a codebook to form a codeword. At block2504, the codeword modification module 2404 may modify or re-order thebit sequence of the codeword based on bad storage location informationof a memory area in which the codeword is to be stored. For example, thecodeword modification module 2404 may swap bits based on numbers of badvariables connected to check nodes of the codebook used to generate theparity bits, based on numbers of bad variables participating in minimalcycles of the codebook used to generate the parity bits, or based onnumbers or a distribution of bad storage locations across storagesub-units, as previously described.

In some example methods, the codeword modification module 2404 may beconfigured to identify the bad storage locations on the fly, such as byaccessing the bad storage database 2406, as part of the encodingprocess. In other example methods, the codeword modification module 2404may have identified the bad storage locations ahead of time and/or bepre-configured with a bit-order modification configuration that includesinformation indicating which bits to swap for a given memory area. Forexample, during a programming operation, the codeword modificationmodule 2404 may be configured to identify the memory area in which thecodeword is to be stored. Based on identifying the memory area, thecodeword modification module may know which bits to swap withoutnecessarily having to access the bad storage database 2406. In someexample configurations, the pre-configuration may occur during amanufacturing phase of the memory system 100, during which the badstorage locations for each of the memory areas of the memory dies 104may be identified. In turn, for one or more particular codebooks to beused to perform the encoding and decoding, bit swapping schemes (orbit-order modification configurations) may be identified for each of thememory areas. The codeword modification module 2404 may be configuredwith the bit swapping schemes. Then, during normal operation, thecodeword modification module 2404 may be configured to identify whichbits to swap based on the bit swapping schemes.

At block 2506, the modified codeword may be stored in the memory area.At block 2508, the modified codeword may be read from the memory area,such as in response to a host read request. At block 2510, the codewordmodification module 2404 may re-order the modified codeword to be in itsoriginal bit sequence. At block 2512, the decoder module 2408 may decodethe re-ordered codeword.

Lastly, as mentioned above, any suitable type of memory can be used.Semiconductor memory devices include volatile memory devices, such asdynamic random access memory (“DRAM”) or static random access memory(“SRAM”) devices, non-volatile memory devices, such as resistive randomaccess memory (“ReRAM”), electrically erasable programmable read onlymemory (“EEPROM”), flash memory (which can also be considered a subsetof EEPROM), ferroelectric random access memory (“FRAM”), andmagnetoresistive random access memory (“MRAM”), and other semiconductorelements capable of storing information. Each type of memory device mayhave different configurations. For example, flash memory devices may beconfigured in a NAND or a NOR configuration.

The memory devices can be formed from passive and/or active elements, inany combinations. By way of non-limiting example, passive semiconductormemory elements include ReRAM device elements, which in some embodimentsinclude a resistivity switching storage element, such as an anti-fuse,phase change material, etc., and optionally a steering element, such asa diode, etc. Further by way of non-limiting example, activesemiconductor memory elements include EEPROM and flash memory deviceelements, which in some embodiments include elements containing a chargestorage region, such as a floating gate, conductive nanoparticles, or acharge storage dielectric material.

Multiple memory elements may be configured so that they are connected inseries or so that each element is individually accessible. By way ofnon-limiting example, flash memory devices in a NAND configuration (NANDmemory) typically contain memory elements connected in series. A NANDmemory array may be configured so that the array is composed of multiplestrings of memory in which a string is composed of multiple memoryelements sharing a single bit line and accessed as a group.Alternatively, memory elements may be configured so that each element isindividually accessible, e.g., a NOR memory array. NAND and NOR memoryconfigurations are exemplary, and memory elements may be otherwiseconfigured.

The semiconductor memory elements located within and/or over a substratemay be arranged in two or three dimensions, such as a two dimensionalmemory structure or a three dimensional memory structure.

In a two dimensional memory structure, the semiconductor memory elementsare arranged in a single plane or a single memory device level.Typically, in a two dimensional memory structure, memory elements arearranged in a plane (e.g., in an x-z direction plane) which extendssubstantially parallel to a major surface of a substrate that supportsthe memory elements. The substrate may be a wafer over or in which thelayer of the memory elements are formed or it may be a carrier substratewhich is attached to the memory elements after they are formed. As anon-limiting example, the substrate may include a semiconductor such assilicon.

The memory elements may be arranged in the single memory device level inan ordered array, such as in a plurality of rows and/or columns.However, the memory elements may be arrayed in non-regular ornon-orthogonal configurations. The memory elements may each have two ormore electrodes or contact lines, such as bit lines and word lines.

A three dimensional memory array is arranged so that memory elementsoccupy multiple planes or multiple memory device levels, thereby forminga structure in three dimensions (i.e., in the x, y and z directions,where the y direction is substantially perpendicular and the x and zdirections are substantially parallel to the major surface of thesubstrate).

As a non-limiting example, a three dimensional memory structure may bevertically arranged as a stack of multiple two dimensional memory devicelevels. As another non-limiting example, a three dimensional memoryarray may be arranged as multiple vertical columns (e.g., columnsextending substantially perpendicular to the major surface of thesubstrate, i.e., in the y direction) with each column having multiplememory elements in each column. The columns may be arranged in a twodimensional configuration, e.g., in an x-z plane, resulting in a threedimensional arrangement of memory elements with elements on multiplevertically stacked memory planes. Other configurations of memoryelements in three dimensions can also constitute a three dimensionalmemory array.

By way of non-limiting example, in a three dimensional NAND memoryarray, the memory elements may be coupled together to form a NAND stringwithin a single horizontal (e.g., x-z) memory device levels.Alternatively, the memory elements may be coupled together to form avertical NAND string that traverses across multiple horizontal memorydevice levels. Other three dimensional configurations can be envisionedwherein some NAND strings contain memory elements in a single memorylevel while other strings contain memory elements which span throughmultiple memory levels. Three dimensional memory arrays may also bedesigned in a NOR configuration and in a ReRAM configuration.

Typically, in a monolithic three dimensional memory array, one or morememory device levels are formed above a single substrate. Optionally,the monolithic three dimensional memory array may also have one or morememory layers at least partially within the single substrate. As anon-limiting example, the substrate may include a semiconductor such assilicon. In a monolithic three dimensional array, the layersconstituting each memory device level of the array are typically formedon the layers of the underlying memory device levels of the array.However, layers of adjacent memory device levels of a monolithic threedimensional memory array may be shared or have intervening layersbetween memory device levels.

Then again, two dimensional arrays may be formed separately and thenpackaged together to form a non-monolithic memory device having multiplelayers of memory. For example, non-monolithic stacked memories can beconstructed by forming memory levels on separate substrates and thenstacking the memory levels atop each other. The substrates may bethinned or removed from the memory device levels before stacking, but asthe memory device levels are initially formed over separate substrates,the resulting memory arrays are not monolithic three dimensional memoryarrays. Further, multiple two dimensional memory arrays or threedimensional memory arrays (monolithic or non-monolithic) may be formedon separate chips and then packaged together to form a stacked-chipmemory device.

Associated circuitry is typically required for operation of the memoryelements and for communication with the memory elements. As non-limitingexamples, memory devices may have circuitry used for controlling anddriving memory elements to accomplish functions such as programming andreading. This associated circuitry may be on the same substrate as thememory elements and/or on a separate substrate. For example, acontroller for memory read-write operations may be located on a separatecontroller chip and/or on the same substrate as the memory elements.

It is intended that the foregoing detailed description be understood asan illustration of selected forms that the invention can take and not asa definition of the invention. It is only the following claims,including all equivalents, that are intended to define the scope of theclaimed invention. Finally, it should be noted that any aspect of any ofthe preferred embodiments described herein can be used alone or incombination with one another.

We claim:
 1. A codebook evaluation method comprising: identifying, withat least one controller, a first optimal codebook for encoding data tobe stored in a first memory area of a memory of a storage device, thefirst optimal codebook identified from among a plurality of codebooksstored in a codebook library; identifying, with the at least onecontroller, a second optimal codebook among the plurality of codebooksfor encoding data to be stored in a second memory area of the memory,the second memory area having different bad storage locations than thefirst memory area; and storing, in a codebook database of the storagedevice, the first optimal codebook, the second optimal codebook, andinformation associating the first optimal codebook with the first memoryarea and the second optimal codebook with the second memory area.
 2. Thecodebook evaluation method of claim 1, further comprising: programming,with the at least one controller, first data into the first memory areausing the plurality of codebooks; after programming the first data,reading, with the at least one controller, the first data from the firstmemory area and decoding, with the at least one controller, the firstdata using the plurality of codebooks; and identifying, with the atleast one controller, decoding metrics associated with each of theplurality of codebooks for the first memory area based on the decoding,wherein identifying the first optimal codebook comprises identifying thefirst optimal codebook from the plurality of codebooks based on thedecoding metrics.
 3. The codebook evaluation method of claim 2, furthercomprising: after identifying the first optimal codebook, detecting,with the at least one controller, a triggering event that triggers theat least one controller to check whether a codebook more optimal thanthe first optimal codebook is stored in the codebook database; inresponse to the detecting, encoding, with the at least one controller,test data with one or more other codebooks in the codebook databaseother than the first optimal codebook; programming, with the at leastone controller, the encoded test data into a test area of the firstmemory area; decoding, with the at least one controller, the encodedtest data using the one or more other codebooks; determining, with theat least one controller, that a codebook of the one or more othercodebooks provides better decoding metrics than the first optimalcodebook for the first memory area; and updating, with the at least onecontroller, the codebook database to indicate to encode futureinformation bit sequences to be stored in the first memory area with thecodebook of the one or more other codebooks instead of the first optimalcodebook.
 4. The codebook evaluation method of claim 1, furthercomprising: identifying, with the at least one controller, bad storagelocation information of the first memory area; scoring, with the atleast one controller, the plurality of codebooks in the codebook libraryfor the first memory area based on the bad storage location informationof the first memory area; and identifying, with the at least onecontroller, that the first optimal codebook has a best score among theplurality of codebooks in the codebook library for the first memoryarea, wherein identifying the first optimal codebook for the firstmemory area is based on identifying that the first optimal codebook hasthe best score.
 5. The codebook evaluation method of claim 4, whereinscoring the plurality of codebooks comprises: for each codebook of theplurality of codebooks, calculating, with the at least one controller,expected contributions to a decoding error probability of a cycle setfor connections of variable nodes and check nodes.
 6. The codebookevaluation method of claim 5, wherein calculating the expectedcontributions to a decoding error probability comprises calculating theexpected contributions with the codebooks in their lifted form.
 7. Thecodebook evaluation method of claim 5, wherein calculating the expectedcontributions to a decoding error probability is based on different biterasure probability values depending on whether associated variablenodes are good variable nodes or bad variable nodes.
 8. The codebookevaluation method of claim 7, wherein calculating the expectedcontributions to a decoding error probability comprises, for a givenexpected contribution calculation corresponding to a given variable nodeconnected to a given check node, selecting, with the at least onecontroller, a high erasure probability value where the given variablenode is a bad variable node and a low erasure probability value wherethe given variable node is a good variable node.
 9. The codebookevaluation method of claim 1, wherein the first memory area and thesecond memory area are part of a plurality of different memory areas,the different memory areas comprising different dies, different planes,different blocks, different pages, or different segments of the memory.10. A system comprising: a memory comprising a first memory area and asecond memory area, the second memory area having different bad storagelocations than the first memory area; and a controller configured to:identify a first optimal codebook from among a plurality of codebooks ina codebook library for encoding data to be stored in the first memoryarea; identify a second optimal codebook from among the plurality ofcodebooks for encoding data to be stored in the second memory area;store the first optimal codebook and the second optimal codebook in acodebook database accessible by the controller when programming datainto the first and second memory areas; and store informationassociating the first optimal codebook with the first memory area andthe second optimal codebook with the second memory area in the codebookdatabase.
 11. The system of claim 10, wherein the controller is furtherconfigured to: program a data set into the first memory area using theplurality of codebooks; after programming the data set, read the dataset from the first memory area and decode the data set using theplurality of codebooks; identify decoding metrics associated with eachof the plurality of codebooks for the first memory area based on thedecoding; and identify the first optimal codebook based on the decodingmetrics.
 12. The system of claim 11, wherein the controller is furtherconfigured to: after identifying the first optimal codebook, detect atriggering event to check whether a codebook more optimal than the firstoptimal codebook is stored in the codebook database; in response to thedetection, encode test data with one or more other codebooks in thecodebook database other than the first optimal codebook; program theencoded test data into a test area of the first memory area; decode theencoded test data using the one or more other codebooks; determine thata codebook of the one or more other codebooks provides better decodingmetrics than the first optimal codebook for the first memory area; andupdate the codebook database to indicate to encode future informationbit sequences to be stored in the first memory area with the codebook ofthe one or more other codebooks instead of the first optimal codebook.13. The system of claim 12, wherein the controller is further configuredto: identify bad storage location information of the first memory area;score the plurality of codebooks in the codebook library for the firstmemory area based on the bad storage location information of the firstmemory area; identify that the first optimal codebook has a best scoreamong the plurality of codebooks in the codebook library for the firstmemory area; and identify the first optimal codebook for the firstmemory area based on identification of the best score.
 14. The system ofclaim 13, wherein the controller is further configured to: for eachcodebook of the plurality of codebooks, calculate expected contributionsto a decoding error probability of a cycle set for connections ofvariable nodes and check nodes in order to score the plurality ofcodebooks.
 15. The system of claim 14, wherein the controller is furtherconfigured to calculate the expected contributions with the codebooks intheir lifted form.
 16. The system of claim 14, wherein the controller isconfigured to calculate the expected contributions based on differentbit erasure probability values depending on whether associated variablenodes are good variable nodes or bad variable nodes.
 17. The system ofclaim 16, wherein calculating the expected contributions to a decodingerror probability comprises, for a given expected contributioncalculation corresponding to a given variable node connected to a givencheck node, selecting, with the at least one controller, a high erasureprobability value where the given variable node is a bad variable nodeand a low erasure probability value where the given variable node is agood variable node.
 18. The system of claim 10, wherein the first memoryarea and the second memory area are part of a plurality of differentmemory areas, the different memory areas comprising different dies,different planes, different blocks, different pages, or differentsegments of the memory.